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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@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},
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PAGES = {xii+261},
ISBN = {2-85629-164-3},
MRCLASS = {14F42 (11J91 14C25 19E15)},
MRNUMBER = {2005k:14041},
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} -
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VENUE={{B}erkeley, {CA},
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SERIES = {Math. Sci. Res. Inst. Publ.},
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AUTHOR = {Drinfel'd, V. G.},
TITLE = {Quantum groups},
BOOKTITLE = {Proc. {I}nternat. {C}ongress of {M}athematicians, {V}ol. {\rm 1, 2}},
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MRCLASS = {17B50 (16A24 17B65 57T05 58F07 82A05 82A15)},
MRNUMBER = {89f:17017},
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} -
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TITLE = {The multiple zeta value algebra and the stable derivation algebra},
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FJOURNAL = {Kyoto University. Research Institute for Mathematical Sciences. Publications},
VOLUME = {39},
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NUMBER = {4},
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ISSN = {0034-5318},
CODEN = {KRMPBV},
MRCLASS = {11M41 (14G32)},
MRNUMBER = {2005h:11196},
URL = {http://projecteuclid.org/getRecord?id=euclid.prims/1145476044},
ZBLNUMBER = {1115.11055},
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author= {Furusho, Hidekazu},
TITLE={Multiple zeta values and Grothendieck-Teichmüller groups},
JOURNAL={Amer. Math. Sci. Contemp. Math.},
VOLUME={416},
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{II}}},
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YEAR = {1995},
MRCLASS = {12F10 (20F36 57M07)},
MRNUMBER = {97c:12003},
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MRREVIEWER = {Daniel Conduch{é}},
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ZBLNUMBER = {0817.18007},
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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},
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CODEN = {INVMBH},
MRCLASS = {20E18 (14E20 20J06)},
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@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},
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PAGES = {xii+314},
ISBN = {0-387-98403-8},
MRCLASS = {18-02},
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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},
}
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