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|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Jan 15 2000|
All Science Journal Classification (ASJC) codes