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.
1
University of Geneva, Section of Mathematics, C.P. 64, 2-4 rue du Lièvre, 1211 Genève 4, Switzerland
Anton Alekseev; Emanuela 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/JOLT_2006_16_3_a5/
@article{JOLT_2006_16_3_a5,
author = {Anton Alekseev and Emanuela 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/JOLT_2006_16_3_a5/}
}
TY - JOUR
AU - Anton Alekseev
AU - Emanuela Petracci
TI - Low Order Terms of the Campbell-Hausdorff Series and the Kashiwara-Vergne Conjecture
JO - Journal of Lie Theory
PY - 2006
SP - 531
EP - 538
VL - 16
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a5/
ID - JOLT_2006_16_3_a5
ER -
%0 Journal Article
%A Anton Alekseev
%A Emanuela Petracci
%T Low Order Terms of the Campbell-Hausdorff Series and the Kashiwara-Vergne Conjecture
%J Journal of Lie Theory
%D 2006
%P 531-538
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2006_16_3_a5/
%F JOLT_2006_16_3_a5
