Journal of Lie Theory 16 (2006), No. 3, 531--538
Copyright Heldermann Verlag 2006
Low Order Terms of the Campbell-Hausdorff Series and the Kashiwara-Vergne Conjecture
Anton Alekseev
University of Geneva, Section of Mathematics, C.P. 64, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Anton.Alekseev@math.unige.ch
Emanuela Petracci
University of Geneva, Section of Mathematics, C.P. 64, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Emanuela.Petracci@math.unige.ch
The Kashiwara-Vergne conjecture states that the Campbell-Hausdorff series of a Lie algebra can be written using a certain couple of functions. In this paper we consider universal solutions which apply to every real finite-dimensional Lie algebra. We prove that a universal solution of the Kashiwara-Vergne conjecture verifying that a natural symmetry condition is unique up to order one. In the Appendix by the second author, this result is used to show that the solutions of the Kashiwara-Vergne conjecture for a quadratic Lie algebra which exist in literature are not universal.
Keywords: Kashiwara-Vergne conjecture, Campbell-Hausdorff series, free Lie algebras, Bernoulli numbers.
MSC: 22E60, 33B10; 17B01
[ Fulltext-pdf (170 KB)] for subscribers only.