Geodesic
Low Order Terms of the Campbell-Hausdorff Series and the Kashiwara-Vergne Conjecture
Journal of Lie theory, Tome 16 (2006) no. 3, pp. 531-538
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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.
Classification : 22E60, 33B10, 17B01
Mots-clés : Kashiwara-Vergne conjecture, Campbell-Hausdorff series, free Lie algebras, Bernoulli numbers 
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     author = {A. Alekseev and E. Petracci},
     title = {Low {Order} {Terms} of the {Campbell-Hausdorff} {Series} and the {Kashiwara-Vergne} {Conjecture}},
     journal = {Journal of Lie theory},
     pages = {531--538},
     year = {2006},
     volume = {16},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a5/}
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A. Alekseev; E. Petracci. Low Order Terms of the Campbell-Hausdorff Series and the Kashiwara-Vergne Conjecture. Journal of Lie theory, Tome 16 (2006) no. 3, pp. 531-538. http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a5/