Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations

@article{Alekseev2009DrinfeldAB,
  title={Drinfeld associators, Braid groups and explicit solutions of the Kashiwara–Vergne equations},
  author={A. Alekseev and Benjamin Enriquez and Charles Torossian},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2009},
  volume={112},
  pages={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… 

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