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

2001/04/09 by Martin Andler, Siddhartha Sahi, Andler, Martin +3
Mathematics · #22 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:22

paper · pdf · doi:10.48550/arxiv.math/0104100

22 pages

arxiv created 2001/04/09 · arxiv updated 2009/11/30

Abstract

Consider the Kontsevich ⋆-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 ⋆-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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• Sur les distributions covariantes dans les algèbres de Lie réductives