2011

Four groups related to associators

Furusho, Hidekazu

Understand

This is a report on associators which is based on my talk at the Mathematische Arbeitstagung in Bonn, June 2011.

I first recall Drinfeld's definition of associators and explain my (and its related) results in arXiv:math/0702128 and arXiv:0808.0319.
Then I explain recent developments on the four pro-unipotent algebraic groups related to associators; the motivic Galois group, the Grothendieck-Teichmuller group, the double shuffle group and the Kashiwara-Vergne group.

Kashiwara, M. and Vergne, M.; The Campbell-Hausdorff formula and invariant hyperfunctions
1978
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Grothendieck, A.; Esquisse d’un programme
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Drinfel’d, V. G.; On quasitriangular quasi-Hopf algebras and a group closely connected with Gal ⁡ ( Q ¯ / Q ) {\rm Gal}(\overline{Q}/{Q})
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Kontsevich, M.; Vassiliev’s knot invariants
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Le, T.Q.T. and Murakami, J.; The universal Vassiliev-Kontsevich invariant for framed oriented links
1996
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by same author; Kontsevich’s integral for the Kauffman polynomial
1996
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by same author; Non-associative tangles
1997
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Racinet, G.; Doubles melanges des polylogarithmes multiples aux racines de l’unite
2002
Cited alongside, same era.
Furusho, H.; The multiple zeta value algebra and the stable derivation algebra
2003
Cited alongside, same era.
by same author; p p -adic multiple zeta values I – p p -adic multiple polylogarithms and the p p -adic KZ equation
2004
Cited alongside, same era.
by same authorand Goncharov, A.; Groupes fondamentaux motiviques de Tate mixte
2005
Cited alongside, same era.
by same authorand Meinrenken, E.; On the Kashiwara-Vergne conjecture
2006
Cited alongside, same era.
Besser, A. and Furusho, H.; The double shuffle relations for p p -adic multiple zeta values
2006
Cited alongside, same era.
Ihara, K., Kaneko, M. and Zagier, D.; Derivation and double shuffle relations for multiple zeta values
2006
Cited alongside, same era.
Terasoma, T.; Geometry of multiple zeta values
2006
Cited alongside, same era.
Enriquez, B.; Quasi-reflection algebras and cyclotomic associators
2007
Cited alongside, same era.
by same author; p p -adic multiple zeta values II – tannakian interpretations
2007
Cited alongside, same era.
by same authorand Jafari, A.; Regularization and generalized double shuffle relations for p p -adic multiple zeta values
2007
Cited alongside, same era.
by same authorand Torossian, C.; The Kashiwara-Vergne conjecture and Drinfeld’s associators
Cited in the paper.

Alekseev, A., Enriquez, B. and Torossian, C.; Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations
2010
Later among the works it cites.
by same authorand Dancso, Z.; Pentagon and hexagon equations following Furusho
Original
2010
Later among the works it cites.
by same author; Pentagon and hexagon equations
2010
Later among the works it cites.
by same author; Geometric interpretation of double shuffle relation for multiple L L -values
Original
2010
Later among the works it cites.
Willwacher, T.; M. Kontsevich’s graph complex and the Grothendieck-Teichmueller Lie algebra
Original
2010
Later among the works it cites.
Zagier, D.; Evaluation of the multiple zeta values ζ ⁡ ( 2 , … , 2 , 3 , 2 , … , 2 ) \zeta(2,...,2,3,2,...,2)
2010
Later among the works it cites.
Brown, F.; Mixed Tate Motives over Spec( Z Z )
Original
2011
Closest in time.
by same authorand Furusho, H.; Mixed Pentagon, octagon and Broadhurst duality equation
Original
2011
Closest in time.
by same author; Double shuffle relation for associators
2011
Closest in time.
Schneps, L.; Double shuffle and Kashiwara-Vergne Lie algebra
2011
Closest in time.

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