# nLab Kashiwara-Vergne conjecture

Quoting the seminar page,

The Kashiwara-Vergne conjecture is a subtle property of the Campbell-Hausdorff series which implies that the Duflo isomorphism theorem can be extended to the germs of bi-invariant distributions on a Lie group. This problem is related to the combinatorics of multiple zeta values and to the Deligne-Drinfeld conjecture. It is also related to some open questions in deformation quantization. An important corollary of the Kashiwara-Vergne conjecture was proved in papers of M. Andler, A. Dvorsky, S. Sahi, and C. Torossian. For an arbitrary Lie algebra the conjecture was established by A. Alekseev and E. Meinrenken. A. Alekseev and C. Torossian built a nice algebraic framework for the Kashiwara-Vergne problem. Using this framework they showed that solutions of the Kashiwara-Vergne problem are closely related to Drinfeld’s associators. In fact, starting from any Drinfeld associator one can produce a solution of the Kashiwara-Vergne problem.

• M. Kashiwara, M. Vergne, The Campbell-Hausdorff formula and invariant hyperfunctions, Inventiones math. 47, 249–272 (1978) pdf
• Anton Alekseev, Charles Torossian, On the Kashiwara-Vergne conjecture, Invent. Math. 164(3), 615–634 (2006) doi; The Kashiwara-Vergne conjecture and Drinfeld’s associators, Ann. of Math. 175:2 (2012) 415–463 pdf; Kontsevich deformation quantization and flat connections arxiv/0906.0187 doi
• A. Alekseev, B. Enriquez, C. Torossian, Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations, Publ. Math. IHES 112 (2010), 143–189 arxiv/0903.4067
• M. Andler, A. Dvorsky, S. Sahi, Kontsevich quantization and invariant distributions on Lie groups, arxiv/9910104
• M. Andler, S. Sahi, C. Torossian, Convolution of invariant distributions: proof of the Kashiwara-Vergne conjecture, math.QA/0104100
• D. Bar-Natan, On associators and the Grothendieck-Teichmuller Group I, q-alg/9606021
• V.G. Drinfeld, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $Gal(\bar{\mathbf{Q}}/\mathbf{Q})$, (Russian) Algebra i Analiz 2:4, 149–181 (1990); translation in Leningrad Math. J. 2:4, 829–860 (1991)
• Thomas Willwacher, M. Kontsevich’s graph complex and the Grothendieck-Teichmueller Lie algebra arxiv/1009.1654
• Maria Podkopaeva, On the Jacobson element and generators of the Lie algebra arxiv/0812.0772
• Anton Alekseev, Florian Naef, Xiaomeng Xu, Chenchang Zhu, Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators, Letters in Mathematical Physics 108:3 (2018) 757–778 doi

Last revised on October 21, 2019 at 12:41:52. See the history of this page for a list of all contributions to it.