Voir la notice de l'article provenant de la source Numdam
The Kashiwara–Vergne (KV) conjecture states the existence of solutions of a pair of equations related with the Campbell–Baker–Hausdorff series. It was solved by Meinrenken and the first author over ℝ, and in a formal version, by two of the authors over a field of characteristic 0. In this paper, we give a simple and explicit formula for a map from the set of Drinfeld associators to the set of solutions of the formal KV equations. Both sets are torsors under the actions of prounipotent groups, and we show that this map is a morphism of torsors. When specialized to the KZ associator, our construction yields a solution over ℝ of the original KV conjecture.
@article{PMIHES_2010__112__143_0,
author = {Alekseev, A. and Enriquez, B. and Torossian, C.},
title = {Drinfeld associators, {Braid} groups and explicit solutions of the {Kashiwara{\textendash}Vergne} equations},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {143--189},
publisher = {Springer-Verlag},
volume = {112},
year = {2010},
doi = {10.1007/s10240-010-0029-4},
mrnumber = {2737979},
zbl = {1238.17008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0029-4/}
}
TY - JOUR AU - Alekseev, A. AU - Enriquez, B. AU - Torossian, C. TI - Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations JO - Publications Mathématiques de l'IHÉS PY - 2010 SP - 143 EP - 189 VL - 112 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0029-4/ DO - 10.1007/s10240-010-0029-4 LA - en ID - PMIHES_2010__112__143_0 ER -
%0 Journal Article %A Alekseev, A. %A Enriquez, B. %A Torossian, C. %T Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations %J Publications Mathématiques de l'IHÉS %D 2010 %P 143-189 %V 112 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-010-0029-4/ %R 10.1007/s10240-010-0029-4 %G en %F PMIHES_2010__112__143_0
Alekseev, A.; Enriquez, B.; Torossian, C. Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations. Publications Mathématiques de l'IHÉS, Tome 112 (2010), pp. 143-189. doi: 10.1007/s10240-010-0029-4
Cité par Sources :