Kashiwara Vergne Research Articles

Convolution of Invariant Distributions: Proof of the Kashiwara?Vergne conjecture

Consider the Kontsevich star product on the symmetric algebra of a finite-dimensional Lie algebra g, regarded as the algebra of distributions with support 0 on g. In this Letter, 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.

Poisson geometry and the Kashiwara–Vergne conjecture

We give a Poisson-geometric proof of the Kashiwara–Vergne conjecture for quadratic Lie algebras, based on the equivariant Moser trick. To cite this article: A. Alekseev, E. Meinrenken, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 723–728.