Quantification par déformation et distributions invariantes

Martin Andler; Alexander Dvorsky; Siddhartha Sahi

doi:10.1016/S0764-4442(00)00104-X

Quantification par déformation et distributions invariantes

Translated title of the contribution: Deformation quantization and invariant distributions

Martin Andler, Alexander Dvorsky, Siddhartha Sahi

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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
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	https://doi.org/10.1016/S0764-4442(00)00104-X
State	Published - Jan 15 2000
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1016/S0764-4442(00)00104-X

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AU - Sahi, Siddhartha

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AB - 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.

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Quantification par déformation et distributions invariantes

Abstract

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