Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations
Publications Mathématiques de l'IHÉS, Tome 112 (2010), pp. 143-189.

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.

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     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},
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     url = {http://www.numdam.org/articles/10.1007/s10240-010-0029-4/}
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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. http://www.numdam.org/articles/10.1007/s10240-010-0029-4/

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