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

Andler, Martin; Sahi, Siddhartha; Torossian, Charles

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

Authors

Andler, Martin

Sahi, Siddhartha

Torossian, Charles

Description

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 $G$.
22 pages