Abstract
We study Kontsevich's deformation quantization for the dual of a finite-dimensional Lie algebra g. Regarding elements of S(g) as distributions on g, we show that the *-multiplication operator (r → r * p) is a differential operator with analytic germ at 0. We use this to establish a conjecture of Kashiwara and Vergne which, in turn, gives a new proof of Duflo's result on the local solvability of bi-invariant differential operators on a Lie group.
Translated title of the contribution | Deformation quantization and invariant distributions |
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Original language | French |
Pages (from-to) | 115-120 |
Number of pages | 6 |
Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
Volume | 330 |
Issue number | 2 |
DOIs | |
State | Published - Jan 15 2000 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)