Abstract
The author will prove that Drinfel’d’s pentagon equation implies his two hexagon equations in the Lie algebra, pro-unipotent, pro-$l$ and pro-nilpotent contexts.
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[A] Y. André, Une Introduction aux Motifs (Motifs Purs, Motifs Mixtes, Périodes), Paris: Soc. Math. France, 2004.
@book {A, MRKEY = {2115000},
AUTHOR = {Andr{é},
Yves},
TITLE = {Une Introduction aux Motifs (Motifs Purs, Motifs Mixtes, Périodes)},
SERIES = {Panoramas et Synthèses},
NUMBER = {17},
PUBLISHER = {Soc. Math. France},
ADDRESS = {Paris},
YEAR = {2004},
PAGES = {xii+261},
ISBN = {2-85629-164-3},
MRCLASS = {14F42 (11J91 14C25 19E15)},
MRNUMBER = {2005k:14041},
MRREVIEWER = {Luca Barbieri Viale},
} -
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TITLE = {Le groupe fondamental de la droite projective moins trois points},
BOOKTITLE = {Galois Groups Over $Q$},
VENUE={{B}erkeley, {CA},
1987},
SERIES = {Math. Sci. Res. Inst. Publ.},
NUMBER = {16},
PAGES = {79--297},
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} -
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@inproceedings {Dr86, MRKEY = {934283},
AUTHOR = {Drinfel'd, V. G.},
TITLE = {Quantum groups},
BOOKTITLE = {Proc. {I}nternat. {C}ongress of {M}athematicians, {V}ol. {\rm 1, 2}},
VEUNE={{B}erkeley, {C}alif., 1986},
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YEAR = {1987},
MRCLASS = {17B50 (16A24 17B65 57T05 58F07 82A05 82A15)},
MRNUMBER = {89f:17017},
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} -
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NUMBER = {6},
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@article {Dr, MRKEY = {1080203},
AUTHOR = {Drinfel'd, V. G.},
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JOURNAL = {Algebra i Analiz},
FJOURNAL = {Algebra i Analiz},
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YEAR = {1990},
NUMBER = {4},
PAGES = {149--181},
ISSN = {0234-0852},
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MRNUMBER = {92f:16047},
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[F03]
H. Furusho, "The multiple zeta value algebra and the stable derivation algebra," Publ. Res. Inst. Math. Sci., vol. 39, iss. 4, pp. 695-720, 2003.
@article {F03, MRKEY = {2025460},
AUTHOR = {Furusho, Hidekazu},
TITLE = {The multiple zeta value algebra and the stable derivation algebra},
JOURNAL = {Publ. Res. Inst. Math. Sci.},
FJOURNAL = {Kyoto University. Research Institute for Mathematical Sciences. Publications},
VOLUME = {39},
YEAR = {2003},
NUMBER = {4},
PAGES = {695--720},
ISSN = {0034-5318},
CODEN = {KRMPBV},
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MRNUMBER = {2005h:11196},
URL = {http://projecteuclid.org/getRecord?id=euclid.prims/1145476044},
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[F06] H. Furusho, "Multiple zeta values and Grothendieck-Teichmüller groups," Amer. Math. Sci. Contemp. Math., vol. 416, pp. 49-82, 2006.
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author= {Furusho, Hidekazu},
TITLE={Multiple zeta values and Grothendieck-Teichmüller groups},
JOURNAL={Amer. Math. Sci. Contemp. Math.},
VOLUME={416},
YEAR={2006},
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MRNUMBER={2007k:14041},
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} -
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AUTHOR = {Furusho, Hidekazu},
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{II}}},
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ADDRESS = {Providence, RI},
YEAR = {1995},
MRCLASS = {12F10 (20F36 57M07)},
MRNUMBER = {97c:12003},
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ZBLNUMBER = {0848.11058},
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@article {JS, MRKEY = {1250465},
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NUMBER = {1},
PAGES = {20--78},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {18D10 (19D23 20G05)},
MRNUMBER = {94m:18008},
MRREVIEWER = {Daniel Conduch{é}},
DOI = {10.1006/aima.1993.1055},
ZBLNUMBER = {0817.18007},
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[K] C. Kassel, Quantum Groups, New York: Springer-Verlag, 1995.
@book {K, MRKEY = {1321145},
AUTHOR = {Kassel, Christian},
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SERIES = {Grad. Texts Math.},
NUMBER = {155},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1995},
PAGES = {xii+531},
ISBN = {0-387-94370-6},
MRCLASS = {17B37 (16W30 18D10 20F36 57M25 81R50)},
MRNUMBER = {96e:17041},
MRREVIEWER = {Yu. N. Bespalov},
ZBLNUMBER={0808.17003},
} -
[LM]
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URL = {http://projecteuclid.org/getRecord?id=euclid.nmj/1118772043},
ZBLNUMBER = {0866.57008},
} -
[LS]
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YEAR = {1997},
NUMBER = {3},
PAGES = {571--600},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {20E18 (14E20 20J06)},
MRNUMBER = {98j:20032},
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ZBLNUMBER={0883.20016},
} -
[M] S. Mac Lane, Categories for the Working Mathematician, Second ed., New York: Springer-Verlag, 1998.
@book {M, MRKEY = {1712872},
AUTHOR = {Mac Lane, Saunders},
TITLE = {Categories for the Working Mathematician},
SERIES = {Graduate Texts in Mathematics},
NUMBER = {5},
EDITION = {Second},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1998},
PAGES = {xii+314},
ISBN = {0-387-98403-8},
MRCLASS = {18-02},
MRNUMBER = {2001j:18001},
ZBLNUMBER = {0906.18001},
ZBLNUMBER = {0232.18001},
} -
[S] L. Schneps, "The Grothendieck-Teichmüller group $\widehat{ GT}$: a survey," in Geometric Galois Actions, 1, Cambridge: Cambridge Univ. Press, 1997, pp. 183-203.
@incollection {S, MRKEY = {1483118},
AUTHOR = {Schneps, Leila},
TITLE = {The {G}rothendieck-{T}eichmüller group {$\widehat{\rm GT}$}: a survey},
BOOKTITLE = {Geometric {G}alois Actions, {\rm 1}},
SERIES = {London Math. Soc. Lecture Note Ser.},
NUMBER = {242},
PAGES = {183--203},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {1997},
MRCLASS = {14H55 (14F35 14L30 20F38)},
MRNUMBER = {99a:14043},
MRREVIEWER = {Athanase Papadopoulos},
ZBLNUMBER={0910.20019},
}