Abstract
It is shown that if $A$ is a separable, exact C$^*$-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then $A$ admits a trace-preserving embedding into a simple, unital AF-algebra with a unique trace. Modulo the UCT, this provides an abstract characterization of C$^*$-subalgebras of simple, unital AF-algebras.
As a consequence, for a countable, discrete, amenable group $G$ acting on a second countable, locally compact, Hausdorff space $X$, $C_0(X) \rtimes _r G$ embeds into a simple, unital AF-algebra if, and only if, $X$ admits a faithful, invariant, Borel, probability measure. Also, for any countable, discrete, amenable group $G$, the reduced group C$^*$-algebra $\mathrm {C}^*_r(G)$ admits a trace-preserving embedding into the universal UHF-algebra.
-
[Alfsen]
E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York-Heidelberg, 1971, vol. 57.
@BOOK{Alfsen,
author = {Alfsen, Erik M.},
title = {Compact Convex Sets and Boundary Integrals},
series = {Ergeb. Math. Grenzgeb.},
volume={57},
publisher = {Springer-Verlag, New York-Heidelberg},
year = {1971},
pages = {x+210},
mrclass = {46A99 (46E05)},
mrnumber = {0445271},
mrreviewer = {H. E. Lacey},
zblnumber = {0209.42601},
doi = {10.1007/978-3-642-65009-3},
url = {https://doi.org/10.1007/978-3-642-65009-3},
} -
[Blackadar:KTheory] B. Blackadar, $K$-Theory for Operator Algebras, Second ed., Cambridge Univ. Press, Cambridge, 1998, vol. 5.
@BOOK{Blackadar:KTheory,
author = {Blackadar, Bruce},
title = {{$K$}-Theory for {O}perator {A}lgebras},
series = {Math. Sci. Res. Inst. Publ.},
volume = {5},
edition = {Second},
publisher = {Cambridge Univ. Press, Cambridge},
year = {1998},
pages = {xx+300},
isbn = {0-521-63532-2},
mrclass = {46L80 (19Kxx 58G12)},
mrnumber = {1656031},
zblnumber = {0913.46054},
} -
[Blackadar:Encyclopedia]
B. Blackadar, Operator Algebras: Theory of $\mathrm{C}^*$-Algebras and von Neumann Algebras, Operator Algebras and Non-commutative Geometry, III, Springer-Verlag, Berlin, 2006, vol. 122.
@BOOK{Blackadar:Encyclopedia,
author = {Blackadar, Bruce},
title = {Operator Algebras: Theory of {$\mathrm{C}^*$}-Algebras and von Neumann Algebras, Operator Algebras and Non-commutative Geometry, III},
series = {Encyclopaedia Math. Sci.},
volume = {122},
publisher = {Springer-Verlag, Berlin},
year = {2006},
pages = {xx+517},
isbn = {978-3-540-28486-4; 3-540-28486-9},
mrclass = {46L05 (46L10 46L80)},
mrnumber = {2188261},
mrreviewer = {Paul Jolissaint},
doi = {10.1007/3-540-28517-2},
url = {https://doi.org/10.1007/3-540-28517-2},
zblnumber = {1092.46003},
} -
[BlackadarKirchberg:MFAlgebras]
B. Blackadar and E. Kirchberg, "Generalized inductive limits of finite-dimensional $\mathrm{C}^*$-algebras," Math. Ann., vol. 307, iss. 3, pp. 343-380, 1997.
@ARTICLE{BlackadarKirchberg:MFAlgebras,
author = {Blackadar, Bruce and Kirchberg, Eberhard},
title = {Generalized inductive limits of finite-dimensional {$\mathrm{C}^*$}-algebras},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {307},
year = {1997},
number = {3},
pages = {343--380},
issn = {0025-5831},
mrclass = {46L05 (46L35)},
mrnumber = {1437044},
mrreviewer = {Terry A. Loring},
doi = {10.1007/s002080050039},
url = {https://doi.org/10.1007/s002080050039},
zblnumber = {0874.46036},
} -
[BBSTWW]
J. Bosa, N. P. Brown, Y. Sato, A. Tikuisis, S. White, and W. Winter, "Covering dimension of $\mathrm{C}^*$-algebras and 2-coloured classification," Mem. Amer. Math. Soc., vol. 257, iss. 1233, p. vii, 2019.
@ARTICLE{BBSTWW,
author = {Bosa, Joan and Brown, Nathanial P. and Sato, Yasuhiko and Tikuisis, Aaron and White, Stuart and Winter, Wilhelm},
title = {Covering dimension of {$\mathrm{C}^*$}-algebras and 2-coloured classification},
journal = {Mem. Amer. Math. Soc.},
fjournal = {Memoirs of the American Mathematical Society},
volume = {257},
year = {2019},
number = {1233},
pages = {vii+97},
issn = {0065-9266},
isbn = {978-1-4704-3470-0; 978-1-4704-4949-0},
mrclass = {46L05 (46L35)},
mrnumber = {3908669},
mrreviewer = {Hiroyuki Osaka},
zblnumber = {07069168},
doi = {10.1090/memo/1233},
url = {https://doi.org/10.1090/memo/1233},
} -
[BrownPedersen:RealRankZero]
L. G. Brown and G. K. Pedersen, "$\mathrm{C}^*$-algebras of real rank zero," J. Funct. Anal., vol. 99, iss. 1, pp. 131-149, 1991.
@ARTICLE{BrownPedersen:RealRankZero,
author = {Brown, Lawrence G. and Pedersen, Gert K.},
title = {{$\mathrm{C}^*$}-algebras of real rank zero},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {99},
year = {1991},
number = {1},
pages = {131--149},
issn = {0022-1236},
mrclass = {46L05 (46L85)},
mrnumber = {1120918},
mrreviewer = {Gerard J. Murphy},
doi = {10.1016/0022-1236(91)90056-B},
url = {https://doi.org/10.1016/0022-1236(91)90056-B},
zblnumber = {0776.46026},
} -
[Brown:AFE]
N. P. Brown, "AF embeddability of crossed products of AF algebras by the integers," J. Funct. Anal., vol. 160, iss. 1, pp. 150-175, 1998.
@ARTICLE{Brown:AFE,
author = {Brown, Nathanial P.},
title = {A{F} embeddability of crossed products of {AF} algebras by the integers},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {160},
year = {1998},
number = {1},
pages = {150--175},
issn = {0022-1236},
mrclass = {46L80 (46L05 46L55)},
mrnumber = {1658700},
mrreviewer = {Valentin Deaconu},
doi = {10.1006/jfan.1998.3339},
url = {https://doi.org/10.1006/jfan.1998.3339},
zblnumber = {0931.46043},
} -
[Brown:UHF]
N. P. Brown, "Crossed products of UHF algebras by some amenable groups," Hokkaido Math. J., vol. 29, iss. 1, pp. 201-211, 2000.
@ARTICLE{Brown:UHF,
author = {Brown, Nathanial P.},
title = {Crossed products of {UHF} algebras by some amenable groups},
journal = {Hokkaido Math. J.},
fjournal = {Hokkaido Mathematical Journal},
volume = {29},
year = {2000},
number = {1},
pages = {201--211},
issn = {0385-4035},
mrclass = {46L55 (19K56 46L80)},
mrnumber = {1745510},
mrreviewer = {Valentin Deaconu},
doi = {10.14492/hokmj/1350912964},
url = {https://doi.org/10.14492/hokmj/1350912964},
zblnumber = {0962.46047},
} -
[Brown:Memoirs]
N. P. Brown, "Invariant means and finite representation theory of $\mathrm{C}^*$-algebras," Mem. Amer. Math. Soc., vol. 184, iss. 865, p. viii, 2006.
@ARTICLE{Brown:Memoirs,
author = {Brown, Nathanial P.},
title = {Invariant means and finite representation theory of {$\mathrm{C}^*$}-algebras},
journal = {Mem. Amer. Math. Soc.},
fjournal = {Memoirs of the American Mathematical Society},
volume = {184},
year = {2006},
number = {865},
pages = {viii+105},
issn = {0065-9266},
mrclass = {46L05 (46L35)},
mrnumber = {2263412},
mrreviewer = {Narutaka Ozawa},
doi = {10.1090/memo/0865},
url = {https://doi.org/10.1090/memo/0865},
zblnumber = {1111.46030},
} -
[BrownOzawa]
N. P. Brown and N. Ozawa, $\mathrm{C}^*$-Algebras and Finite-Dimensional Approximations, Amer. Math. Soc., Providence, RI, 2008, vol. 88.
@BOOK{BrownOzawa,
author = {Brown, Nathanial P. and Ozawa, Narutaka},
title = {{$\mathrm{C}^*$}-Algebras and Finite-Dimensional Approximations},
series = {Grad. Stud. in Math.},
volume = {88},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2008},
pages = {xvi+509},
isbn = {978-0-8218-4381-9; 0-8218-4381-8},
mrclass = {46L05 (43A07 46-02 46L10)},
mrnumber = {2391387},
mrreviewer = {Mikael R\o rdam},
doi = {10.1090/gsm/088},
url = {https://doi.org/10.1090/gsm/088},
zblnumber = {1160.46001},
} -
[ClarkHuefSims]
L. O. Clark, A. an Huef, and A. Sims, "AF-embeddability of 2-graph algebras and quasidiagonality of $k$-graph algebras," J. Funct. Anal., vol. 271, iss. 4, pp. 958-991, 2016.
@ARTICLE{ClarkHuefSims,
author = {Clark, Lisa Orloff and an Huef, Astrid and Sims, Aidan},
title = {A{F}-embeddability of 2-graph algebras and quasidiagonality of {$k$}-graph algebras},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {271},
year = {2016},
number = {4},
pages = {958--991},
issn = {0022-1236},
mrclass = {46L05},
mrnumber = {3507995},
mrreviewer = {Hiroyuki Osaka},
doi = {10.1016/j.jfa.2016.04.024},
url = {https://doi.org/10.1016/j.jfa.2016.04.024},
zblnumber = {1358.46051},
} -
[Connes:InjectiveFactors]
A. Connes, "Classification of injective factors. Cases $\mathrm{II}_{1},$ $\mathrm{II}_{\infty },$ $\mathrm{III}_{\lambda },$ $\lambda \not=1$," Ann. of Math. (2), vol. 104, iss. 1, pp. 73-115, 1976.
@ARTICLE{Connes:InjectiveFactors,
author = {Connes, A.},
title = {Classification of injective factors. {C}ases {$\mathrm{II}\sb{1},
$} {$\mathrm{II}\sb{\infty },
$} {$\mathrm{III}\sb{\lambda },
$} {$\lambda \not=1$}},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {104},
year = {1976},
number = {1},
pages = {73--115},
issn = {0003-486X},
mrclass = {46L10},
mrnumber = {0454659},
mrreviewer = {François Combes},
doi = {10.2307/1971057},
url = {https://doi.org/10.2307/1971057},
zblnumber = {0343.46042},
} -
[CuipercaGiordanoNgNiu]
A. Ciuperca, T. Giordano, P. W. Ng, and Z. Niu, "Amenability and uniqueness," Adv. Math., vol. 240, pp. 325-345, 2013.
@ARTICLE{CuipercaGiordanoNgNiu,
author = {Ciuperca, A. and Giordano, T. and Ng, P. W. and Niu, Z.},
title = {Amenability and uniqueness},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {240},
year = {2013},
pages = {325--345},
issn = {0001-8708},
mrclass = {46L35 (46L05 46L10)},
mrnumber = {3046312},
mrreviewer = {Esteban Andruchow},
doi = {10.1016/j.aim.2013.02.018},
url = {https://doi.org/10.1016/j.aim.2013.02.018},
zblnumber = {1292.46036},
} -
[CuntzHigson:KupiersTheorem]
J. Cuntz and N. Higson, "Kuiper’s theorem for Hilbert modules," in Operator Algebras and Mathematical Physics, Amer. Math. Soc., Providence, RI, 1987, vol. 62, pp. 429-435.
@INCOLLECTION{CuntzHigson:KupiersTheorem,
author = {Cuntz, Joachim and Higson, Nigel},
title = {Kuiper's theorem for {H}ilbert modules},
booktitle = {Operator Algebras and Mathematical Physics},
venue = {{I}owa {C}ity, {I}owa, 1985},
series = {Contemp. Math.},
volume = {62},
pages = {429--435},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1987},
mrclass = {46L05 (46L80)},
mrnumber = {0878392},
mrreviewer = {Vern Paulsen},
doi = {10.1090/conm/062/878392},
url = {https://doi.org/10.1090/conm/062/878392},
zblnumber = {0616.46066},
} -
[Dadarlat:QDMorphisms]
M. Dadarlat, "Quasidiagonal morphisms and homotopy," J. Funct. Anal., vol. 151, iss. 1, pp. 213-233, 1997.
@ARTICLE{Dadarlat:QDMorphisms,
author = {Dadarlat, Marius},
title = {Quasidiagonal morphisms and homotopy},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {151},
year = {1997},
number = {1},
pages = {213--233},
issn = {0022-1236},
mrclass = {46L05 (46L85)},
mrnumber = {1487776},
mrreviewer = {Hiroshi Takai},
doi = {10.1006/jfan.1997.3145},
url = {https://doi.org/10.1006/jfan.1997.3145},
zblnumber = {0992.46042},
} -
[Dadarlat:locallyUCT] M. Dadarlat, "Some remarks on the universal coefficient theorem in $KK$-theory," in Operator Algebras and Mathematical Physics, Theta, Bucharest, 2003, pp. 65-74.
@INCOLLECTION{Dadarlat:locallyUCT,
author = {Dadarlat, Marius},
title = {Some remarks on the universal coefficient theorem in {$KK$}-theory},
booktitle = {Operator Algebras and Mathematical Physics},
venue = {{C}onstan\c{t}a, 2001},
pages = {65--74},
publisher = {Theta, Bucharest},
year = {2003},
mrclass = {19K35 (46L80)},
mrnumber = {2018224},
mrreviewer = {Ralf Meyer},
zblnumber = {1284.19008},
} -
[Dadarlat:TAFClassification]
M. Dadarlat, "Morphisms of simple tracially AF algebras," Internat. J. Math., vol. 15, iss. 9, pp. 919-957, 2004.
@ARTICLE{Dadarlat:TAFClassification,
author = {Dadarlat, Marius},
title = {Morphisms of simple tracially {AF} algebras},
journal = {Internat. J. Math.},
fjournal = {International Journal of Mathematics},
volume = {15},
year = {2004},
number = {9},
pages = {919--957},
issn = {0129-167X},
mrclass = {46L05 (19K14 19K35 46L35 46L80)},
mrnumber = {2106154},
mrreviewer = {Xiao Chun Fang},
doi = {10.1142/S0129167X04002636},
url = {https://doi.org/10.1142/S0129167X04002636},
zblnumber = {1071.46036},
} -
[Dadarlat:TopKK]
M. Dadarlat, "On the topology of the Kasparov groups and its applications," J. Funct. Anal., vol. 228, iss. 2, pp. 394-418, 2005.
@ARTICLE{Dadarlat:TopKK,
author = {Dadarlat, Marius},
title = {On the topology of the {K}asparov groups and its applications},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {228},
year = {2005},
number = {2},
pages = {394--418},
issn = {0022-1236},
mrclass = {46L80 (19K35)},
mrnumber = {2175412},
mrreviewer = {Jean-Louis Tu},
doi = {10.1016/j.jfa.2005.02.015},
url = {https://doi.org/10.1016/j.jfa.2005.02.015},
zblnumber = {1088.46042},
} -
[Dadarlat:AFEmbContField]
M. Dadarlat, "On AF embeddability of continuous fields," C. R. Math. Acad. Sci. Soc. R. Can., vol. 31, iss. 1, pp. 16-19, 2009.
@ARTICLE{Dadarlat:AFEmbContField,
author = {Dadarlat, Marius},
title = {On {AF} embeddability of continuous fields},
journal = {C. R. Math. Acad. Sci. Soc. R. Can.},
fjournal = {Comptes Rendus Mathématiques de l'Académie des Sciences. La Société Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada},
volume = {31},
year = {2009},
number = {1},
pages = {16--19},
issn = {0706-1994},
mrclass = {46L05},
mrnumber = {2519017},
zblnumber = {1183.46053},
url = {https://mr.math.ca/article/on-af-embeddability-of-continuous-fields/},
} -
[DadarlatEilers:CuntzPairs]
M. Dadarlat and S. Eilers, "Asymptotic unitary equivalence in $KK$-theory," $K$-Theory, vol. 23, iss. 4, pp. 305-322, 2001.
@ARTICLE{DadarlatEilers:CuntzPairs,
author = {Dadarlat, Marius and Eilers, S{\o{r}}en},
title = {Asymptotic unitary equivalence in {$KK$}-theory},
journal = {$K$-Theory},
fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences},
volume = {23},
year = {2001},
number = {4},
pages = {305--322},
issn = {0920-3036},
mrclass = {19K35 (46L80)},
mrnumber = {1860859},
mrreviewer = {Emmanuel C. Germain},
url = {https://access.portico.org/stable?au=pgh2h1dc9zw},
zblnumber = {0991.19002},
} -
[DadarlatEilers:Classification]
M. Dadarlat and S. Eilers, "On the classification of nuclear $\mathrm{C}^*$-algebras," Proc. London Math. Soc. (3), vol. 85, iss. 1, pp. 168-210, 2002.
@ARTICLE{DadarlatEilers:Classification,
author = {Dadarlat, Marius and Eilers, S{\o{r}}en},
title = {On the classification of nuclear {$\mathrm{C}^*$}-algebras},
journal = {Proc. London Math. Soc. (3)},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
volume = {85},
year = {2002},
number = {1},
pages = {168--210},
issn = {0024-6115},
mrclass = {19K35 (46L05 46L35 46L80)},
mrnumber = {1901373},
mrreviewer = {Emmanuel C. Germain},
doi = {10.1112/S0024611502013679},
url = {https://doi.org/10.1112/S0024611502013679},
zblnumber = {1031.46070},
} -
[Davidson:C*Book]
K. R. Davidson, $\mathrm{C}^*$-Algebras by Example, Amer. Math. Soc., Providence, RI, 1996, vol. 6.
@BOOK{Davidson:C*Book,
author = {Davidson, Kenneth R.},
title = {{$\mathrm{C}^*$}-Algebras by Example},
series = {Fields Inst. Monogr.},
volume = {6},
publisher = {Amer. Math. Soc., Providence, RI},
year = {1996},
pages = {xiv+309},
isbn = {0-8218-0599-1},
mrclass = {46Lxx (46-01)},
mrnumber = {1402012},
mrreviewer = {Robert S. Doran},
doi = {10.1090/fim/006},
url = {https://doi.org/10.1090/fim/006},
zblnumber = {0958.46029},
} -
[Dixmier:C*algebras] J. Dixmier, $C\sp*$-Algebras, North-Holland Publishing Co., New York, 1977, vol. 15.
@BOOK{Dixmier:C*algebras,
author = {Dixmier, Jacques},
title = {{$C\sp*$}-Algebras},
note = {translated from the French by Francis Jellett},
series = {North-Holland Math. Library},
volume = {15},
publisher = {North-Holland Publishing Co., New York},
year = {1977},
pages = {xiii+492},
isbn = {0-7204-0762-1},
mrclass = {46L05},
mrnumber = {0458185},
zblnumber = {0372.46058},
} -
[Effros:Problems]
E. G. Effros, "On the structure theory of $C^{\ast} $-algebras: some old and new problems," in Operator Algebras and Applications, Part I, Amer. Math. Soc., Providence, R.I., 1982, vol. 38, pp. 19-34.
@INCOLLECTION{Effros:Problems,
author = {Effros, Edward G.},
title = {On the structure theory of {$C\sp{\ast} $}-algebras: some old and new problems},
booktitle = {Operator Algebras and Applications, {P}art {I}},
venue = {{K}ingston, {O}nt., 1980},
series = {Proc. Sympos. Pure Math.},
volume = {38},
pages = {19--34},
publisher = {Amer. Math. Soc., Providence, R.I.},
year = {1982},
mrclass = {46Lxx (46Hxx)},
mrnumber = {0679693},
mrreviewer = {G. A. Elliott},
zblnumber = {0506.46044},
doi = {10.1090/pspum/038.1/679693},
url = {https://dx.doi.org/10.1090/pspum/038.1/679693},
} -
[EffrosHandelmanShen]
E. G. Effros, D. E. Handelman, and C. L. Shen, "Dimension groups and their affine representations," Amer. J. Math., vol. 102, iss. 2, pp. 385-407, 1980.
@ARTICLE{EffrosHandelmanShen,
author = {Effros, Edward G. and Handelman, David E. and Shen, Chao Liang},
title = {Dimension groups and their affine representations},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {102},
year = {1980},
number = {2},
pages = {385--407},
issn = {0002-9327},
mrclass = {46L55 (22A26 58G12 82A15)},
mrnumber = {0564479},
mrreviewer = {Alain Connes},
doi = {10.2307/2374244},
url = {https://doi.org/10.2307/2374244},
zblnumber = {0457.46047},
} -
[Elliott:AF]
G. A. Elliott, "On the classification of inductive limits of sequences of semisimple finite-dimensional algebras," J. Algebra, vol. 38, iss. 1, pp. 29-44, 1976.
@ARTICLE{Elliott:AF,
author = {Elliott, George A.},
title = {On the classification of inductive limits of sequences of semisimple finite-dimensional algebras},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {38},
year = {1976},
number = {1},
pages = {29--44},
issn = {0021-8693},
mrclass = {46L05 (16A46)},
mrnumber = {0397420},
mrreviewer = {Horst Behncke},
doi = {10.1016/0021-8693(76)90242-8},
url = {https://doi.org/10.1016/0021-8693(76)90242-8},
zblnumber = {0323.46063},
} -
[Elliott:TotallyOrderedK0]
G. A. Elliott, "On totally ordered groups, and $K_{0}$," in Ring Theory, 1979, pp. 1-49.
@INPROCEEDINGS{Elliott:TotallyOrderedK0,
author = {Elliott, George A.},
title = {On totally ordered groups, and {$K\sb{0}$}},
booktitle = {Ring Theory},
venue = {{P}roc. {C}onf., {U}niv. {W}aterloo, {W}aterloo, 1978},
series = {Lecture Notes in Math.},
volume = {734},
pages = {1--49},
publisher = {Springer, Berlin},
year = {1979},
mrclass = {06F20 (46L05)},
mrnumber = {0548122},
mrreviewer = {P. F. Conrad},
zblnumber = {0418.06010},
doi = {10.1007/BFb0103152},
url = {https://doi.org/10.1007/BFb0103152},
} -
[Elliott:AT]
G. A. Elliott, "On the classification of $\mathrm{C}^*$-algebras of real rank zero," J. Reine Angew. Math., vol. 443, pp. 179-219, 1993.
@ARTICLE{Elliott:AT,
author = {Elliott, George A.},
title = {On the classification of {$\mathrm{C}^*$}-algebras of real rank zero},
journal = {J. Reine Angew. Math.},
fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
volume = {443},
year = {1993},
pages = {179--219},
issn = {0075-4102},
mrclass = {46L05 (19K14 46L80)},
mrnumber = {1241132},
mrreviewer = {Shuang Zhang},
url = {https://www.degruyter.com/view/journals/crll/1993/443/article-p179.xml},
zblnumber = {0809.46067},
} -
[ElliottGongLinNiu] G. A. Elliott, G. Gong, H. Lin, and Z. Niu, On the classification of simple amenable $\mathrm{C}^*$-algebras with finite decomposition rank, II, 2015.
@misc{ElliottGongLinNiu,
author = {Elliott, George A. and Gong, Guihua and Lin, Huaxin and Niu, Zhuang},
title = {On the classification of simple amenable {$\mathrm{C}^*$}-algebras with finite decomposition rank, {II}},
arxiv = {1507.03437},
year = {2015},
} -
[ElliottKucerovsky]
G. A. Elliott and D. Kucerovsky, "An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem," Pacific J. Math., vol. 198, iss. 2, pp. 385-409, 2001.
@ARTICLE{ElliottKucerovsky,
author = {Elliott, George A. and Kucerovsky, Dan},
title = {An abstract {V}oiculescu-{B}rown-{D}ouglas-{F}illmore absorption theorem},
journal = {Pacific J. Math.},
fjournal = {Pacific Journal of Mathematics},
volume = {198},
year = {2001},
number = {2},
pages = {385--409},
issn = {0030-8730},
mrclass = {46L05 (46M20)},
mrnumber = {1835515},
mrreviewer = {Hua Xin Lin},
doi = {10.2140/pjm.2001.198.385},
url = {https://doi.org/10.2140/pjm.2001.198.385},
zblnumber = {1058.46041},
} -
[Gabe:AbsorbingExtensions]
J. Gabe, "A note on nonunital absorbing extensions," Pacific J. Math., vol. 284, iss. 2, pp. 383-393, 2016.
@ARTICLE{Gabe:AbsorbingExtensions,
author = {Gabe, James},
title = {A note on nonunital absorbing extensions},
journal = {Pacific J. Math.},
fjournal = {Pacific Journal of Mathematics},
volume = {284},
year = {2016},
number = {2},
pages = {383--393},
issn = {0030-8730},
mrclass = {46L05 (46L35 46L80)},
mrnumber = {3544306},
mrreviewer = {Tomasz Kania},
doi = {10.2140/pjm.2016.284.383},
url = {https://doi.org/10.2140/pjm.2016.284.383},
zblnumber = {1357.46045},
} -
[Gabe:LiftingTheorems] J. Gabe, Lifting theorems for completely positive maps, 2016.
@MISC{Gabe:LiftingTheorems,
author = {Gabe, James},
title = {Lifting theorems for completely positive maps},
year = {2016},
arxiv = {1508.00389v3},
zblnumber = {},
} -
[Gabe:TWW]
J. Gabe, "Quasidiagonal traces on exact $\mathrm{C}^*$-algebras," J. Funct. Anal., vol. 272, iss. 3, pp. 1104-1120, 2017.
@ARTICLE{Gabe:TWW,
author = {Gabe, James},
title = {Quasidiagonal traces on exact {$\mathrm{C}^*$}-algebras},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {272},
year = {2017},
number = {3},
pages = {1104--1120},
issn = {0022-1236},
mrclass = {46L05 (46L35 46L80)},
mrnumber = {3579134},
mrreviewer = {Bachir Bekka},
doi = {10.1016/j.jfa.2016.10.022},
url = {https://doi.org/10.1016/j.jfa.2016.10.022},
zblnumber = {1369.46046},
} -
[GabeRuiz:AbsorbingCones] J. Gabe and E. Ruiz, Absorbing representations with respect to closed operator convex cones, 2015.
@MISC{GabeRuiz:AbsorbingCones,
author = {Gabe, James and Ruiz, E.},
title = {Absorbing representations with respect to closed operator convex cones},
year = {2015},
arxiv = {1503.07799},
zblnumber = {},
} -
[GongLinNiu] G. Gong, H. Lin, and Z. Niu, Classification of simple amenable $\mathcal{Z}$-stable C$^*$-algebras, 2015.
@MISC{GongLinNiu,
author = {Gong, G. and Lin, H. and Niu, Z.},
title = {Classification of simple amenable {$\mathcal{Z}$}-stable {C}$^*$-algebras},
year = {2015},
arxiv = {1501.00135},
zblnumber = {},
} -
[Haagerup:Quasitrace]
U. Haagerup, "Quasitraces on exact $\mathrm{C}^*$-algebras are traces," C. R. Math. Acad. Sci. Soc. R. Can., vol. 36, iss. 2-3, pp. 67-92, 2014.
@ARTICLE{Haagerup:Quasitrace,
author = {Haagerup, Uffe},
title = {Quasitraces on exact {$\mathrm{C}^*$}-algebras are traces},
journal = {C. R. Math. Acad. Sci. Soc. R. Can.},
fjournal = {Comptes Rendus Mathématiques de l'Académie des Sciences. La Société Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada},
volume = {36},
year = {2014},
number = {2-3},
pages = {67--92},
issn = {0706-1994},
mrclass = {46L35 (46L80)},
mrnumber = {3241179},
mrreviewer = {Francesc Perera},
zblnumber = {1325.46055},
url = {https://mr.math.ca/volume-issue/vol-36-2014/vol-36-2-2014/},
} -
[HaagerupThorbjornsen]
U. Haagerup and S. Thorbjornsen, "A new application of random matrices: ${ Ext}(\mathrm{C}^*_{ red}(F_2))$ is not a group," Ann. of Math. (2), vol. 162, iss. 2, pp. 711-775, 2005.
@ARTICLE{HaagerupThorbjornsen,
author = {Haagerup, Uffe and Thorbj{\o{r}}nsen, Steen},
title = {A new application of random matrices: {${\rm Ext}(\mathrm{C}^*_{\rm red}(F_2))$} is not a group},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {162},
year = {2005},
number = {2},
pages = {711--775},
issn = {0003-486X},
mrclass = {46L54 (15A52 46L35)},
mrnumber = {2183281},
mrreviewer = {Beno\^ıt Collins},
doi = {10.4007/annals.2005.162.711},
url = {https://doi.org/10.4007/annals.2005.162.711},
zblnumber = {1103.46032},
} -
[HarpeSkandalis]
P. de la Harpe and G. Skandalis, "Powers’ property and simple $\mathrm{C}^\ast$-algebras," Math. Ann., vol. 273, iss. 2, pp. 241-250, 1986.
@ARTICLE{HarpeSkandalis,
author = {de la Harpe, Pierre and Skandalis, Georges},
title = {Powers' property and simple {$\mathrm{C}^\ast$}-algebras},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {273},
year = {1986},
number = {2},
pages = {241--250},
issn = {0025-5831},
mrclass = {46L55 (22D25 46L05)},
mrnumber = {0817879},
mrreviewer = {Dana P. Williams},
doi = {10.1007/BF01451404},
url = {https://doi.org/10.1007/BF01451404},
zblnumber = {0563.46033},
} -
[HigsonKasparov:BaumConnes]
N. Higson and G. Kasparov, "$E$-theory and $KK$-theory for groups which act properly and isometrically on Hilbert space," Invent. Math., vol. 144, iss. 1, pp. 23-74, 2001.
@ARTICLE{HigsonKasparov:BaumConnes,
author = {Higson, Nigel and Kasparov, Gennadi},
title = {{$E$}-theory and {$KK$}-theory for groups which act properly and isometrically on {H}ilbert space},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {144},
year = {2001},
number = {1},
pages = {23--74},
issn = {0020-9910},
mrclass = {19K35 (19L47 46L80)},
mrnumber = {1821144},
mrreviewer = {Emmanuel C. Germain},
doi = {10.1007/s002220000118},
url = {https://doi.org/10.1007/s002220000118},
zblnumber = {0988.19003},
} -
[Jones:Subfactors]
V. F. R. Jones, "Index for subfactors," Invent. Math., vol. 72, iss. 1, pp. 1-25, 1983.
@ARTICLE{Jones:Subfactors,
author = {Jones, V. F. R.},
title = {Index for subfactors},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {72},
year = {1983},
number = {1},
pages = {1--25},
issn = {0020-9910},
mrclass = {46L35 (10D07)},
mrnumber = {0696688},
mrreviewer = {Yasuo Watatani},
doi = {10.1007/BF01389127},
url = {https://doi.org/10.1007/BF01389127},
zblnumber = {0508.46040},
} -
[Katsura:AFECuntzFlows]
T. Katsura, "AF-embeddability of crossed products of Cuntz algebras," J. Funct. Anal., vol. 196, iss. 2, pp. 427-442, 2002.
@ARTICLE{Katsura:AFECuntzFlows,
author = {Katsura, Takeshi},
title = {A{F}-embeddability of crossed products of {C}untz algebras},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {196},
year = {2002},
number = {2},
pages = {427--442},
issn = {0022-1236},
mrclass = {46L55 (46L05)},
mrnumber = {1943097},
mrreviewer = {Astrid An Huef},
doi = {10.1016/S0022-1236(02)00003-4},
url = {https://doi.org/10.1016/S0022-1236(02)00003-4},
zblnumber = {1024.46019},
} -
[KerrNowak]
D. Kerr and P. W. Nowak, "Residually finite actions and crossed products," Ergodic Theory Dynam. Systems, vol. 32, iss. 5, pp. 1585-1614, 2012.
@ARTICLE{KerrNowak,
author = {Kerr, David and Nowak, Piotr W.},
title = {Residually finite actions and crossed products},
journal = {Ergodic Theory Dynam. Systems},
fjournal = {Ergodic Theory and Dynamical Systems},
volume = {32},
year = {2012},
number = {5},
pages = {1585--1614},
issn = {0143-3857},
mrclass = {37A55 (22D40 46L55)},
mrnumber = {2974211},
mrreviewer = {Claire Anantharaman-Delaroche},
doi = {10.1017/S0143385711000575},
url = {https://doi.org/10.1017/S0143385711000575},
zblnumber = {1280.37009},
} -
[Kirchberg:FactorizationProperty]
E. Kirchberg, "Discrete groups with Kazhdan’s property ${ T}$ and factorization property are residually finite," Math. Ann., vol. 299, iss. 3, pp. 551-563, 1994.
@ARTICLE{Kirchberg:FactorizationProperty,
author = {Kirchberg, Eberhard},
title = {Discrete groups with {K}azhdan's property {${\rm T}$} and factorization property are residually finite},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {299},
year = {1994},
number = {3},
pages = {551--563},
issn = {0025-5831},
mrclass = {46L05 (22D10 22D25 43A65 46L35 46M07)},
mrnumber = {1282231},
mrreviewer = {Alain Valette},
doi = {10.1007/BF01459798},
url = {https://doi.org/10.1007/BF01459798},
zblnumber = {0805.46066},
} -
[KirchbergRordam:TomsWinterConj]
E. Kirchberg and M. Rordam, "Central sequence $\mathrm{C}^*$-algebras and tensorial absorption of the Jiang-Su algebra," J. Reine Angew. Math., vol. 695, pp. 175-214, 2014.
@ARTICLE{KirchbergRordam:TomsWinterConj,
author = {Kirchberg, Eberhard and R{\o{r}}dam, Mikael},
title = {Central sequence {$\mathrm{C}^*$}-algebras and tensorial absorption of the {J}iang-{S}u algebra},
journal = {J. Reine Angew. Math.},
fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
volume = {695},
year = {2014},
pages = {175--214},
issn = {0075-4102},
mrclass = {46L35 (46C20)},
mrnumber = {3276157},
mrreviewer = {Aurelian Gheondea},
doi = {10.1515/crelle-2012-0118},
url = {https://doi.org/10.1515/crelle-2012-0118},
zblnumber = {1307.46046},
} -
[KirchbergRordam:CentralSequenceAlgebras]
E. Kirchberg and M. Rordam, "When central sequence $\mathrm{C}^*$-algebras have characters," Internat. J. Math., vol. 26, iss. 7, p. 1550049, 2015.
@ARTICLE{KirchbergRordam:CentralSequenceAlgebras,
author = {Kirchberg, Eberhard and R{\o{r}}dam, Mikael},
title = {When central sequence {$\mathrm{C}^*$}-algebras have characters},
journal = {Internat. J. Math.},
fjournal = {International Journal of Mathematics},
volume = {26},
year = {2015},
number = {7},
pages = {1550049, 32},
issn = {0129-167X},
mrclass = {46L35 (46L06)},
mrnumber = {3357038},
mrreviewer = {E. St\o rmer},
doi = {10.1142/S0129167X15500494},
url = {https://doi.org/10.1142/S0129167X15500494},
zblnumber = {1339.46055},
} -
[KucerovskyNg] D. Kucerovsky and P. W. Ng, "The corona factorization property and approximate unitary equivalence," Houston J. Math., vol. 32, iss. 2, pp. 531-550, 2006.
@ARTICLE{KucerovskyNg,
author = {Kucerovsky, Dan and Ng, P. W.},
title = {The corona factorization property and approximate unitary equivalence},
journal = {Houston J. Math.},
fjournal = {Houston Journal of Mathematics},
volume = {32},
year = {2006},
number = {2},
pages = {531--550},
issn = {0362-1588},
mrclass = {46L85 (46L05 46L80)},
mrnumber = {2219330},
mrreviewer = {Vladimir Manuilov},
zblnumber = {1111.46050},
} -
[Lin:BrownPedersen]
H. X. Lin, "Exponential rank of $\mathrm{C}^*$-algebras with real rank zero and the Brown-Pedersen conjectures," J. Funct. Anal., vol. 114, iss. 1, pp. 1-11, 1993.
@ARTICLE{Lin:BrownPedersen,
author = {Lin, Hua Xin},
title = {Exponential rank of {$\mathrm{C}^*$}-algebras with real rank zero and the {B}rown-{P}edersen conjectures},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {114},
year = {1993},
number = {1},
pages = {1--11},
issn = {0022-1236},
mrclass = {46L05 (19K56)},
mrnumber = {1220980},
mrreviewer = {Ronghui Ji},
doi = {10.1006/jfan.1993.1060},
url = {https://doi.org/10.1006/jfan.1993.1060},
zblnumber = {0812.46054},
} -
[Lin:TAF]
H. Lin, "Tracially AF $\mathrm{C}^*$-algebras," Trans. Amer. Math. Soc., vol. 353, iss. 2, pp. 693-722, 2001.
@ARTICLE{Lin:TAF,
author = {Lin, Huaxin},
title = {Tracially {AF} {$\mathrm{C}^*$}-algebras},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {353},
year = {2001},
number = {2},
pages = {693--722},
issn = {0002-9947},
mrclass = {46L35 (46L05)},
mrnumber = {1804513},
mrreviewer = {Kengo Matsumoto},
doi = {10.1090/S0002-9947-00-02680-5},
url = {https://doi.org/10.1090/S0002-9947-00-02680-5},
zblnumber = {0964.46044},
} -
[Lin:StableApproxEquivalence]
H. Lin, "Stable approximate unitary equivalence of homomorphisms," J. Operator Theory, vol. 47, iss. 2, pp. 343-378, 2002.
@ARTICLE{Lin:StableApproxEquivalence,
author = {Lin, Huaxin},
title = {Stable approximate unitary equivalence of homomorphisms},
journal = {J. Operator Theory},
fjournal = {Journal of Operator Theory},
volume = {47},
year = {2002},
number = {2},
pages = {343--378},
issn = {0379-4024},
mrclass = {46L80 (46L05 46L35)},
mrnumber = {1911851},
mrreviewer = {Vladimir Manuilov},
zblnumber = {1029.46097},
url = {http://www.mathjournals.org/jot/2002-047-002/2002-047-002-006.html},
} -
[Lin:TAFClassification]
H. Lin, "Classification of simple $\mathrm{C}^\ast$-algebras of tracial topological rank zero," Duke Math. J., vol. 125, iss. 1, pp. 91-119, 2004.
@ARTICLE{Lin:TAFClassification,
author = {Lin, Huaxin},
title = {Classification of simple {$\mathrm{C}^\ast$}-algebras of tracial topological rank zero},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {125},
year = {2004},
number = {1},
pages = {91--119},
issn = {0012-7094},
mrclass = {46L05 (46L35 46L80)},
mrnumber = {2097358},
mrreviewer = {Hiroyuki Osaka},
doi = {10.1215/S0012-7094-04-12514-X},
url = {https://doi.org/10.1215/S0012-7094-04-12514-X},
zblnumber = {1068.46032},
} -
[Lin:AFEmbAHalg]
H. Lin, "AF-embeddings of the crossed products of AH-algebras by finitely generated abelian groups," International Mathematics Research Papers, vol. 2008, iss. 3, 2008.
@ARTICLE{Lin:AFEmbAHalg,
author = {Lin, Huaxin},
title = {A{F}-embeddings of the crossed products of {AH}-algebras by finitely generated abelian groups},
journal = {International Mathematics Research Papers},
volume={2008},
month={01},
year = {2008},
number = {3},
doi = {10.1093/imrp/rpn007},
url = {https://doi.org/10.1093/imrp/rpn007},
note = {rpn007},
issn = {1687-3017},
mrclass = {46L55 (22D25 46L05 46L35)},
mrnumber = {2457848},
mrreviewer = {Francesc Perera},
zblnumber = {1166.46040},
} -
[Luck:TraceConjecture]
W. Lück, "The relation between the Baum-Connes conjecture and the trace conjecture," Invent. Math., vol. 149, iss. 1, pp. 123-152, 2002.
@ARTICLE{Luck:TraceConjecture,
author = {Lück, Wolfgang},
title = {The relation between the {B}aum-{C}onnes conjecture and the trace conjecture},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {149},
year = {2002},
number = {1},
pages = {123--152},
issn = {0020-9910},
mrclass = {19K56 (46L85 58J22)},
mrnumber = {1914619},
mrreviewer = {Evgeniy V. Troitskiĭ},
doi = {10.1007/s002220200215},
url = {https://doi.org/10.1007/s002220200215},
zblnumber = {1035.19003},
} -
[Matui:AFE]
M. Hiroki, "AF embeddability of crossed products of AT algebras by the integers and its application," J. Funct. Anal., vol. 192, iss. 2, pp. 562-580, 2002.
@ARTICLE{Matui:AFE,
author = {Hiroki, Matui},
title = {A{F} embeddability of crossed products of {AT} algebras by the integers and its application},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {192},
year = {2002},
number = {2},
pages = {562--580},
issn = {0022-1236},
mrclass = {46L55 (46L05)},
mrnumber = {1923414},
mrreviewer = {Masaharu Kusuda},
doi = {10.1006/jfan.2001.3911},
url = {https://doi.org/10.1006/jfan.2001.3911},
zblnumber = {1021.46048},
} -
[MatuiSato:ZStable]
H. Matui and Y. Sato, "Strict comparison and $\mathcal{Z}$-absorption of nuclear $\mathrm{C}^*$-algebras," Acta Math., vol. 209, iss. 1, pp. 179-196, 2012.
@ARTICLE{MatuiSato:ZStable,
author = {Matui, Hiroki and Sato, Yasuhiko},
title = {Strict comparison and {$\mathcal{Z}$}-absorption of nuclear {$\mathrm{C}^*$}-algebras},
journal = {Acta Math.},
fjournal = {Acta Mathematica},
volume = {209},
year = {2012},
number = {1},
pages = {179--196},
issn = {0001-5962},
mrclass = {46L05},
mrnumber = {2979512},
mrreviewer = {Caleb Eckhardt},
doi = {10.1007/s11511-012-0084-4},
url = {https://doi.org/10.1007/s11511-012-0084-4},
zblnumber = {1277.46028},
} -
[MatuiSato:DecompositionRank]
H. Matui and Y. Sato, "Decomposition rank of UHF-absorbing $\mathrm{C}^*$-algebras," Duke Math. J., vol. 163, iss. 14, pp. 2687-2708, 2014.
@ARTICLE{MatuiSato:DecompositionRank,
author = {Matui, Hiroki and Sato, Yasuhiko},
title = {Decomposition rank of {UHF}-absorbing {$\mathrm{C}^*$}-algebras},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {163},
year = {2014},
number = {14},
pages = {2687--2708},
issn = {0012-7094},
mrclass = {46L06 (46L35 46L55)},
mrnumber = {3273581},
mrreviewer = {William Paschke},
doi = {10.1215/00127094-2826908},
url = {https://doi.org/10.1215/00127094-2826908},
zblnumber = {1317.46041},
} -
[Mingo:KupiersTheorem]
J. A. Mingo, "$K$-theory and multipliers of stable $\mathrm{C}^\ast$-algebras," Trans. Amer. Math. Soc., vol. 299, iss. 1, pp. 397-411, 1987.
@ARTICLE{Mingo:KupiersTheorem,
author = {Mingo, J. A.},
title = {{$K$}-theory and multipliers of stable {$\mathrm{C}^\ast$}-algebras},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {299},
year = {1987},
number = {1},
pages = {397--411},
issn = {0002-9947},
mrclass = {46L80 (18F25 19K56 46M20)},
mrnumber = {0869419},
mrreviewer = {Judith A. Packer},
doi = {10.2307/2000501},
url = {https://doi.org/10.2307/2000501},
zblnumber = {0616.46067},
} -
[MvN:RingsOfOperatorsIV]
F. J. Murray and J. von Neumann, "On rings of operators. IV," Ann. of Math. (2), vol. 44, pp. 716-808, 1943.
@ARTICLE{MvN:RingsOfOperatorsIV,
author = {Murray, F. J. and von Neumann, J.},
title = {On rings of operators. {IV}},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {44},
year = {1943},
pages = {716--808},
issn = {0003-486X},
mrclass = {46.0X},
mrnumber = {0009096},
mrreviewer = {E. R. Lorch},
doi = {10.2307/1969107},
url = {https://doi.org/10.2307/1969107},
zblnumber = {0060.26903},
} -
[OrtegaPereraRordamI]
E. Ortega, F. Perera, and M. Rordam, "The Corona Factorization Property and refinement monoids," Trans. Amer. Math. Soc., vol. 363, iss. 9, pp. 4505-4525, 2011.
@ARTICLE{OrtegaPereraRordamI,
author = {Ortega, Eduard and Perera, Francesc and R{\o{r}}dam, Mikael},
title = {The {C}orona {F}actorization {P}roperty and refinement monoids},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {363},
year = {2011},
number = {9},
pages = {4505--4525},
issn = {0002-9947},
mrclass = {46L35 (06F05 46L80)},
mrnumber = {2806681},
mrreviewer = {Xiao Chun Fang},
doi = {10.1090/S0002-9947-2011-05480-2},
url = {https://doi.org/10.1090/S0002-9947-2011-05480-2},
zblnumber = {1235.46057},
} -
[OrtegaPereraRordamII]
E. Ortega, F. Perera, and M. Rordam, "The Corona Factorization Property, stability, and the Cuntz semigroup of a $\mathrm{C}^\ast$-algebra," Int. Math. Res. Not. IMRN, iss. 1, pp. 34-66, 2012.
@ARTICLE{OrtegaPereraRordamII,
author = {Ortega, Eduard and Perera, Francesc and R{\o{r}}dam, Mikael},
title = {The {C}orona {F}actorization {P}roperty, stability, and the {C}untz semigroup of a {$\mathrm{C}^\ast$}-algebra},
journal = {Int. Math. Res. Not. IMRN},
fjournal = {International Mathematics Research Notices. IMRN},
year = {2012},
number = {1},
pages = {34--66},
issn = {1073-7928},
mrclass = {46L35 (06F05 46L05 46L80)},
mrnumber = {2874927},
mrreviewer = {Aaron Tikuisis},
doi = {10.1093/imrn/rnr013},
url = {https://doi.org/10.1093/imrn/rnr013},
zblnumber = {1245.46049},
} -
[Ozawa:Cone]
N. Ozawa, "Homotopy invariance of AF-embeddability," Geom. Funct. Anal., vol. 13, iss. 1, pp. 216-222, 2003.
@ARTICLE{Ozawa:Cone,
author = {Ozawa, N.},
title = {Homotopy invariance of {AF}-embeddability},
journal = {Geom. Funct. Anal.},
fjournal = {Geometric and Functional Analysis},
volume = {13},
year = {2003},
number = {1},
pages = {216--222},
issn = {1016-443X},
mrclass = {46L05},
mrnumber = {1978495},
mrreviewer = {William Paschke},
doi = {10.1007/s000390300005},
url = {https://doi.org/10.1007/s000390300005},
zblnumber = {1028.46090},
} -
[Ozawa:DixmierApproximation]
N. Ozawa, "Dixmier approximation and symmetric amenability for $\mathrm{C}^*$-algebras," J. Math. Sci. Univ. Tokyo, vol. 20, iss. 3, pp. 349-374, 2013.
@ARTICLE{Ozawa:DixmierApproximation,
author = {Ozawa, Narutaka},
title = {Dixmier approximation and symmetric amenability for {$\mathrm{C}^*$}-algebras},
journal = {J. Math. Sci. Univ. Tokyo},
fjournal = {The University of Tokyo. Journal of Mathematical Sciences},
volume = {20},
year = {2013},
number = {3},
pages = {349--374},
issn = {1340-5705},
mrclass = {46L05 (46L10)},
mrnumber = {3156986},
mrreviewer = {William Paschke},
zblnumber = {1300.46049},
url = {https://www.ms.u-tokyo.ac.jp/journal/abstract/jms200303.html},
} -
[OzawaRordamSato]
N. Ozawa, M. Rordam, and Y. Sato, "Elementary amenable groups are quasidiagonal," Geom. Funct. Anal., vol. 25, iss. 1, pp. 307-316, 2015.
@ARTICLE{OzawaRordamSato,
author = {Ozawa, Narutaka and R{\o{r}}dam, Mikael and Sato, Yasuhiko},
title = {Elementary amenable groups are quasidiagonal},
journal = {Geom. Funct. Anal.},
fjournal = {Geometric and Functional Analysis},
volume = {25},
year = {2015},
number = {1},
pages = {307--316},
issn = {1016-443X},
mrclass = {46L35 (43A07)},
mrnumber = {3320894},
mrreviewer = {Stefanos Orfanos},
doi = {10.1007/s00039-015-0315-x},
url = {https://doi.org/10.1007/s00039-015-0315-x},
zblnumber = {1335.46053},
} -
[Pimsner:AFE]
M. V. Pimsner, "Embedding some transformation group $C^{\ast} $-algebras into AF-algebras," Ergodic Theory Dynam. Systems, vol. 3, iss. 4, pp. 613-626, 1983.
@ARTICLE{Pimsner:AFE,
author = {Pimsner, Mihai V.},
title = {Embedding some transformation group {$C\sp{\ast} $}-algebras into {AF}-algebras},
journal = {Ergodic Theory Dynam. Systems},
fjournal = {Ergodic Theory and Dynamical Systems},
volume = {3},
year = {1983},
number = {4},
pages = {613--626},
issn = {0143-3857},
mrclass = {46L05 (57S05)},
mrnumber = {0753927},
mrreviewer = {G. A. Elliott},
doi = {10.1017/S0143385700002182},
url = {https://doi.org/10.1017/S0143385700002182},
zblnumber = {0582.46063},
} -
[PimsnerVoiculescu]
M. V. Pimsner and D. Voiculescu, "Imbedding the irrational rotation $C^{\ast} $-algebra into an AF-algebra," J. Operator Theory, vol. 4, iss. 2, pp. 201-210, 1980.
@ARTICLE{PimsnerVoiculescu,
author = {Pimsner, Mihai V. and Voiculescu, D.},
title = {Imbedding the irrational rotation {$C\sp{\ast} $}-algebra into an {AF}-algebra},
journal = {J. Operator Theory},
fjournal = {Journal of Operator Theory},
volume = {4},
year = {1980},
number = {2},
pages = {201--210},
issn = {0379-4024},
mrclass = {46L35 (16A54)},
mrnumber = {0595412},
mrreviewer = {David Handelman},
zblnumber = {0525.46031},
url = {http://www.mathjournals.org/jot/1980-004-002/1980-004-002-003.html},
} -
[Popa:Quasidiagonality]
S. Popa, "On local finite-dimensional approximation of $\mathrm{C}^*$-algebras," Pacific J. Math., vol. 181, iss. 1, pp. 141-158, 1997.
@ARTICLE{Popa:Quasidiagonality,
author = {Popa, Sorin},
title = {On local finite-dimensional approximation of {$\mathrm{C}^*$}-algebras},
journal = {Pacific J. Math.},
fjournal = {Pacific Journal of Mathematics},
volume = {181},
year = {1997},
number = {1},
pages = {141--158},
issn = {0030-8730},
mrclass = {46L05},
mrnumber = {1491038},
mrreviewer = {Sze-Kai Tsui},
doi = {10.2140/pjm.1997.181.141},
url = {https://doi.org/10.2140/pjm.1997.181.141},
zblnumber = {0907.46046},
} -
[Rainone:MF]
T. Rainone, "MF actions and $K$-theoretic dynamics," J. Funct. Anal., vol. 267, iss. 2, pp. 542-578, 2014.
@ARTICLE{Rainone:MF,
author = {Rainone, Timothy},
title = {M{F} actions and {$K$}-theoretic dynamics},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {267},
year = {2014},
number = {2},
pages = {542--578},
issn = {0022-1236},
mrclass = {46L55 (46L80)},
mrnumber = {3210039},
mrreviewer = {Xiao Chun Fang},
doi = {10.1016/j.jfa.2014.04.005},
url = {https://doi.org/10.1016/j.jfa.2014.04.005},
zblnumber = {1304.37027},
} -
[RainoneSchafhauser]
T. Rainone and C. Schafhauser, "Crossed products of nuclear $\mathrm{C}^*$-algebras and their traces," Adv. Math., vol. 347, pp. 105-149, 2019.
@ARTICLE{RainoneSchafhauser,
author = {Rainone, Timothy and Schafhauser, Christopher},
title = {Crossed products of nuclear {$\mathrm{C}^*$}-algebras and their traces},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {347},
year = {2019},
pages = {105--149},
issn = {0001-8708},
mrclass = {46L05},
mrnumber = {3915315},
mrreviewer = {Scott M. LaLonde},
doi = {10.1016/j.aim.2019.01.045},
url = {https://doi.org/10.1016/j.aim.2019.01.045},
zblnumber = {07044289},
} -
[Rieffel:StableRank]
M. A. Rieffel, "Dimension and stable rank in the $K$-theory of $C^{\ast}$-algebras," Proc. London Math. Soc. (3), vol. 46, iss. 2, pp. 301-333, 1983.
@ARTICLE{Rieffel:StableRank,
author = {Rieffel, Marc A.},
title = {Dimension and stable rank in the {$K$}-theory of {$C\sp{\ast}$}-algebras},
journal = {Proc. London Math. Soc. (3)},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
volume = {46},
year = {1983},
number = {2},
pages = {301--333},
issn = {0024-6115},
mrclass = {46L05 (46H20 46M20)},
mrnumber = {0693043},
mrreviewer = {David Handelman},
doi = {10.1112/plms/s3-46.2.301},
url = {https://doi.org/10.1112/plms/s3-46.2.301},
zblnumber = {0533.46046},
} -
[Rordam:UHFStable]
M. Rordam, "On the structure of simple $\mathrm{C}^*$-algebras tensored with a UHF-algebra," J. Funct. Anal., vol. 100, iss. 1, pp. 1-17, 1991.
@ARTICLE{Rordam:UHFStable,
author = {R{\o{r}}dam, Mikael},
title = {On the structure of simple {$\mathrm{C}^*$}-algebras tensored with a {UHF}-algebra},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {100},
year = {1991},
number = {1},
pages = {1--17},
issn = {0022-1236},
mrclass = {46L05},
mrnumber = {1124289},
mrreviewer = {Mahmood Khoshkam},
doi = {10.1016/0022-1236(91)90098-P},
url = {https://doi.org/10.1016/0022-1236(91)90098-P},
zblnumber = {0773.46028},
} -
[Rordam:UHFStable2]
M. Rordam, "On the structure of simple $\mathrm{C}^*$-algebras tensored with a UHF-algebra. II," J. Funct. Anal., vol. 107, iss. 2, pp. 255-269, 1992.
@ARTICLE{Rordam:UHFStable2,
author = {R{\o{r}}dam, Mikael},
title = {On the structure of simple {$\mathrm{C}^*$}-algebras tensored with a {UHF}-algebra. {II}},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {107},
year = {1992},
number = {2},
pages = {255--269},
issn = {0022-1236},
mrclass = {46L05 (46L85)},
mrnumber = {1172023},
mrreviewer = {Mahmood Khoshkam},
doi = {10.1016/0022-1236(92)90106-S},
url = {https://doi.org/10.1016/0022-1236(92)90106-S},
zblnumber = {0810.46067},
} -
[Rordam:YellowBook]
M. Rordam, "Classification of nuclear, simple $\mathrm{C}^*$-algebras," in Classification of Nuclear $\mathrm{C}^*$-Algebras. Entropy in Operator Algebras, Springer, Berlin, 2002, vol. 126, pp. 1-145.
@INCOLLECTION{Rordam:YellowBook,
author = {R{\o{r}}dam, Mikael},
title = {Classification of nuclear, simple {$\mathrm{C}^*$}-algebras},
booktitle = {Classification of Nuclear {$\mathrm{C}^*$}-Algebras. {E}ntropy in Operator Algebras},
series = {Encyclopaedia Math. Sci.},
volume = {126},
pages = {1--145},
publisher = {Springer, Berlin},
year = {2002},
mrclass = {46L05 (19K56 46L35 46L80)},
mrnumber = {1878882},
mrreviewer = {Judith A. Packer},
doi = {10.1007/978-3-662-04825-2_1},
url = {https://doi.org/10.1007/978-3-662-04825-2_1},
zblnumber = {1016.46037},
} -
[RosenbergSchochet]
J. Rosenberg and C. Schochet, "The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized $K$-functor," Duke Math. J., vol. 55, iss. 2, pp. 431-474, 1987.
@ARTICLE{RosenbergSchochet,
author = {Rosenberg, Jonathan and Schochet, Claude},
title = {The {K}ünneth theorem and the universal coefficient theorem for {K}asparov's generalized {$K$}-functor},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {55},
year = {1987},
number = {2},
pages = {431--474},
issn = {0012-7094},
mrclass = {46L80 (19K33 46M20 58G12)},
mrnumber = {0894590},
mrreviewer = {Thierry Fack},
doi = {10.1215/S0012-7094-87-05524-4},
url = {https://doi.org/10.1215/S0012-7094-87-05524-4},
zblnumber = {0644.46051},
} -
[Sakai] S. Sakai, $C\sp*$-Algebras and $W\sp*$-Algebras, Springer-Verlag, New York, 1971, vol. 60.
@BOOK{Sakai,
author = {Sakai, Shôichirô},
title = {{$C\sp*$}-Algebras and {$W\sp*$}-Algebras},
series = {Ergeb. Math. Grenzgeb.},
volume = {60},
publisher = {Springer-Verlag, New York},
year = {1971},
pages = {xii+253},
mrclass = {46L05 (46L10)},
mrnumber = {0442701},
mrreviewer = {Richard I. Loebl},
zblnumber = {0219.46042},
} -
[Sato:TomsWinter] Y. Sato, Trace spaces of simple nuclear C$^*$-algebras with finite-dimensional extreme boundary, 2012.
@MISC{Sato:TomsWinter,
author = {Sato, Yasuhiko},
title = {Trace spaces of simple nuclear {C}$^*$-algebras with finite-dimensional extreme boundary},
year = {2012},
arxiv = {1209.3000v1},
zblnumber = {},
} -
[SatoWhiteWinter]
Y. Sato, S. White, and W. Winter, "Nuclear dimension and $\mathcal{Z}$-stability," Invent. Math., vol. 202, iss. 2, pp. 893-921, 2015.
@ARTICLE{SatoWhiteWinter,
author = {Sato, Yasuhiko and White, Stuart and Winter, Wilhelm},
title = {Nuclear dimension and {$\mathcal{Z}$}-stability},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {202},
year = {2015},
number = {2},
pages = {893--921},
issn = {0020-9910},
mrclass = {46L35 (45L05)},
mrnumber = {3418247},
mrreviewer = {Aaron Tikuisis},
doi = {10.1007/s00222-015-0580-1},
url = {https://doi.org/10.1007/s00222-015-0580-1},
zblnumber = {1350.46040},
} -
[Schafhauser:Graph1]
C. Schafhauser, "AF-embeddings of graph $\mathrm{C}^*$-algebras," J. Operator Theory, vol. 74, iss. 1, pp. 177-182, 2015.
@ARTICLE{Schafhauser:Graph1,
author = {Schafhauser, Christopher},
title = {A{F}-embeddings of graph {$\mathrm{C}^*$}-algebras},
journal = {J. Operator Theory},
fjournal = {Journal of Operator Theory},
volume = {74},
year = {2015},
number = {1},
pages = {177--182},
issn = {0379-4024},
mrclass = {46L05},
mrnumber = {3383619},
mrreviewer = {Aljaž Zalar},
doi = {10.7900/jot.2014may23.2017},
url = {https://doi.org/10.7900/jot.2014may23.2017},
zblnumber = {1389.46059},
} -
[Schafhauser:Crelle]
C. Schafhauser, "A new proof of the Tikuisis–White–Winter theorem," J. Reine Angew. Math., vol. 759, pp. 291-304, 2020.
@article{Schafhauser:Crelle,
author = {Schafhauser, Christopher},
TITLE = {A new proof of the {T}ikuisis--{W}hite--{W}inter theorem},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
VOLUME = {759},
YEAR = {2020},
PAGES = {291--304},
ISSN = {0075-4102},
MRCLASS = {46L05 (46L30)},
MRNUMBER = {4058182},
DOI = {10.1515/crelle-2017-0056},
URL = {https://doi.org/10.1515/crelle-2017-0056},
zblnumber = {07167735},
} -
[Schafhauser:MF] C. Schafhauser, MF traces and the Cuntz semigroup, 2017.
@MISC{Schafhauser:MF,
author = {Schafhauser, Christopher},
title = {{MF} traces and the {C}untz semigroup},
arxiv = {1705.06555},
year = {2017},
} -
[Skandalis:KKnuc]
G. Skandalis, "Une notion de nucléarité en $K$-théorie (d’après J. Cuntz)," $K$-Theory, vol. 1, iss. 6, pp. 549-573, 1988.
@ARTICLE{Skandalis:KKnuc,
author = {Skandalis, Georges},
title = {Une notion de nucléarité en {$K$}-théorie (d'après {J}. {C}untz)},
journal = {$K$-Theory},
fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences},
volume = {1},
year = {1988},
number = {6},
pages = {549--573},
issn = {0920-3036},
mrclass = {46L80 (19K33 46L05 46M20)},
mrnumber = {0953916},
mrreviewer = {J. A. Mingo},
url = {https://access.portico.org/stable?au=pgg197fsmh5},
zblnumber = {0653.46065},
} -
[Spielberg:AFE]
J. S. Spielberg, "Embedding $\mathrm{C}^*$-algebra extensions into $AF$ algebras," J. Funct. Anal., vol. 81, iss. 2, pp. 325-344, 1988.
@ARTICLE{Spielberg:AFE,
author = {Spielberg, John S.},
title = {Embedding {$\mathrm{C}^*$}-algebra extensions into {$AF$} algebras},
journal = {J. Funct. Anal.},
fjournal = {Journal of Functional Analysis},
volume = {81},
year = {1988},
number = {2},
pages = {325--344},
issn = {0022-1236},
mrclass = {46L05 (46L80)},
mrnumber = {0971884},
mrreviewer = {Cornel Pasnicu},
doi = {10.1016/0022-1236(88)90104-8},
url = {https://doi.org/10.1016/0022-1236(88)90104-8},
zblnumber = {0678.46047},
} -
[TWW:Annals]
A. Tikuisis, S. White, and W. Winter, "Quasidiagonality of nuclear $\mathrm{C}^\ast$-algebras," Ann. of Math. (2), vol. 185, iss. 1, pp. 229-284, 2017.
@ARTICLE{TWW:Annals,
author = {Tikuisis, Aaron and White, Stuart and Winter, Wilhelm},
title = {Quasidiagonality of nuclear {$\mathrm{C}^\ast$}-algebras},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {185},
year = {2017},
number = {1},
pages = {229--284},
issn = {0003-486X},
mrclass = {46L05 (47L40)},
mrnumber = {3583354},
mrreviewer = {Dinesh Jayantilal Karia},
doi = {10.4007/annals.2017.185.1.4},
url = {https://doi.org/10.4007/annals.2017.185.1.4},
zblnumber = {1367.46044},
} -
[TomsWhiteWinter]
A. S. Toms, S. White, and W. Winter, "$\mathcal{Z}$-stability and finite-dimensional tracial boundaries," Int. Math. Res. Not. IMRN, iss. 10, pp. 2702-2727, 2015.
@ARTICLE{TomsWhiteWinter,
author = {Toms, Andrew S. and White, Stuart and Winter, Wilhelm},
title = {{$\mathcal{Z}$}-stability and finite-dimensional tracial boundaries},
journal = {Int. Math. Res. Not. IMRN},
fjournal = {International Mathematics Research Notices. IMRN},
year = {2015},
number = {10},
pages = {2702--2727},
issn = {1073-7928},
mrclass = {46L35 (46L40)},
mrnumber = {3352253},
mrreviewer = {C. J. K. Batty},
doi = {10.1093/imrn/rnu001},
url = {https://doi.org/10.1093/imrn/rnu001},
zblnumber = {1335.46054},
} -
[TomsWinter:SSA]
A. S. Toms and W. Winter, "Strongly self-absorbing $\mathrm{C}^*$-algebras," Trans. Amer. Math. Soc., vol. 359, iss. 8, pp. 3999-4029, 2007.
@ARTICLE{TomsWinter:SSA,
author = {Toms, Andrew S. and Winter, Wilhelm},
title = {Strongly self-absorbing {$\mathrm{C}^*$}-algebras},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {359},
year = {2007},
number = {8},
pages = {3999--4029},
issn = {0002-9947},
mrclass = {46L05 (46L35)},
mrnumber = {2302521},
mrreviewer = {Hua Xin Lin},
doi = {10.1090/S0002-9947-07-04173-6},
url = {https://doi.org/10.1090/S0002-9947-07-04173-6},
zblnumber = {1120.46046},
} -
[Tu:AmenableGroupoid]
J. Tu, "La conjecture de Baum-Connes pour les feuilletages moyennables," $K$-Theory, vol. 17, iss. 3, pp. 215-264, 1999.
@ARTICLE{Tu:AmenableGroupoid,
author = {Tu, Jean-Louis},
title = {La conjecture de {B}aum-{C}onnes pour les feuilletages moyennables},
journal = {$K$-Theory},
fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences},
volume = {17},
year = {1999},
number = {3},
pages = {215--264},
issn = {0920-3036},
mrclass = {19K35 (46L85 58J22)},
mrnumber = {1703305},
mrreviewer = {Hiroshi Takai},
url = {https://access.portico.org/stable?au=pgh2h1dc844},
zblnumber = {0939.19001},
} -
[Zhang:RieszInterpolation]
S. Zhang, "A Riesz decomposition property and ideal structure of multiplier algebras," J. Operator Theory, vol. 24, iss. 2, pp. 209-225, 1990.
@ARTICLE{Zhang:RieszInterpolation,
author = {Zhang, Shuang},
title = {A {R}iesz decomposition property and ideal structure of multiplier algebras},
journal = {J. Operator Theory},
fjournal = {Journal of Operator Theory},
volume = {24},
year = {1990},
number = {2},
pages = {209--225},
issn = {0379-4024},
mrclass = {46L05},
mrnumber = {1150618},
mrreviewer = {C. J. K. Batty},
zblnumber = {0747.46043},
url = {http://www.mathjournals.org/jot/1990-024-002/1990-024-002-001.html},
}