
Journal of Lie Theory 16 (2006), No. 3, 531538 Copyright Heldermann Verlag 2006 Low Order Terms of the CampbellHausdorff Series and the KashiwaraVergne Conjecture Anton Alekseev University of Geneva, Section of Mathematics, C.P. 64, 24 rue du Lièvre, 1211 Genève 4, Switzerland Anton.Alekseev@math.unige.ch Emanuela Petracci University of Geneva, Section of Mathematics, C.P. 64, 24 rue du Lièvre, 1211 Genève 4, Switzerland Emanuela.Petracci@math.unige.ch The KashiwaraVergne conjecture states that the CampbellHausdorff 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 finitedimensional Lie algebra. We prove that a universal solution of the KashiwaraVergne 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 KashiwaraVergne conjecture for a quadratic Lie algebra which exist in literature are not universal. Keywords: KashiwaraVergne conjecture, CampbellHausdorff series, free Lie algebras, Bernoulli numbers. MSC: 22E60, 33B10; 17B01 [ Fulltextpdf (170 KB)] for subscribers only. 