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.
| 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 |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
Quantification par déformation et distributions invariantes. / Andler, Martin; Dvorsky, Alexander; Sahi, Siddhartha.
In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 330, No. 2, 15.01.2000, p. 115-120.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Quantification par déformation et distributions invariantes
AU - Andler, Martin
AU - Dvorsky, Alexander
AU - Sahi, Siddhartha
PY - 2000/1/15
Y1 - 2000/1/15
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=0034650016&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034650016&partnerID=8YFLogxK
U2 - 10.1016/S0764-4442(00)00104-X
DO - 10.1016/S0764-4442(00)00104-X
M3 - Article
AN - SCOPUS:0034650016
VL - 330
SP - 115
EP - 120
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 2
ER -