Kontsevich quantization and invariant distributions on Lie groups

Details Kontsevich quantization and invariant distributions on Lie groups Kontsevich quantization and invariant distributions on Lie groups

1999-10-20

arxiv.org/abs/math/9910104v1

Mathematics

Quantum Algebra

22 pages, LaTeX. This is an expanded version of math.QA/9905065

Scientific paper

We study Kontsevich's deformation quantization for the dual of a finite-dimensional real Lie algebra (or superalgebra) g. In this case the Kontsevich star-product defines a new convolution on S(g), regarded as the space of distributions supported at 0 in g. For p in S(g), we show that the convolution operator f->f*p is a differential operator with analytic germ. We use this fact to prove a conjecture of Kashiwara and Vergne on invariant distributions on a Lie group. This yields a new proof of Duflo's result on local solvability of bi-invariant differential operators on a Lie group. Moreover, this new proof extends to Lie supergroups.

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