Eulerian idempotent and Kashiwara-Vergne conjecture
Quantum Algebra
2007-05-23 v1
Abstract
By using the interplay of the Eulerian idempotent and the Dynkin idempotent, we construct explicitly a particular symmetric solution (F,G) of the first equation of the Kashiwara-Vergne conjecture: x+y-log(exp(y)exp(x))=(1-exp(-ad x))F(x,y)+(exp(ad y)-1)G(x,y) . Then, we explicit all the solutions of the equation in the completion of the free Lie algebra generated by two indeterminates x and y thanks to the kernel of the Dynkin idempotent.
Cite
@article{arxiv.math/0612548,
title = {Eulerian idempotent and Kashiwara-Vergne conjecture},
author = {Emily Burgunder},
journal= {arXiv preprint arXiv:math/0612548},
year = {2007}
}
Comments
25 pages