Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture

Details Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture

2001-04-09

arxiv.org/abs/math/0104100v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

Consider the Kontsevich $\star$-product on the symmetric algebra of a finite dimensional Lie algebra $\mathfrak g$, regarded as the algebra of distributions with support 0 on $\mathfrak g$. In this paper, we extend this $\star$-product to distributions satisfying an appropriate support condition. As a consequence, we prove a long standing conjecture of Kashiwara-Vergne on the convolution of germs of invariant distributions on the Lie group $G$.

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