Kontsevich quantization and invariant distributions on Lie groups
Martin Andler; Alexander Dvorsky; Siddhartha Sahi
Annales scientifiques de l'École Normale Supérieure (2002)
- Volume: 35, Issue: 3, page 371-390
- ISSN: 0012-9593
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topAndler, Martin, Dvorsky, Alexander, and Sahi, Siddhartha. "Kontsevich quantization and invariant distributions on Lie groups." Annales scientifiques de l'École Normale Supérieure 35.3 (2002): 371-390. <http://eudml.org/doc/82574>.
@article{Andler2002,
author = {Andler, Martin, Dvorsky, Alexander, Sahi, Siddhartha},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {star product; deformation quantization; Kashiwara-Vergne conjecture; invariant distribution; bi-invariant differential operator; Poisson manifolds; Lie superalgebras},
language = {eng},
number = {3},
pages = {371-390},
publisher = {Elsevier},
title = {Kontsevich quantization and invariant distributions on Lie groups},
url = {http://eudml.org/doc/82574},
volume = {35},
year = {2002},
}
TY - JOUR
AU - Andler, Martin
AU - Dvorsky, Alexander
AU - Sahi, Siddhartha
TI - Kontsevich quantization and invariant distributions on Lie groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2002
PB - Elsevier
VL - 35
IS - 3
SP - 371
EP - 390
LA - eng
KW - star product; deformation quantization; Kashiwara-Vergne conjecture; invariant distribution; bi-invariant differential operator; Poisson manifolds; Lie superalgebras
UR - http://eudml.org/doc/82574
ER -
References
top- [1] Kontsevich M., Deformation quantization of Poisson manifolds I, e-print, math.QA/9709040. Zbl1058.53065
- [2] Andler M., Dvorsky A., Sahi S., Deformation quantization and invariant distributions, C. R. Acad. Sci.330 (2000) 115-120. Zbl0957.22022MR1745177
- [3] Arnal D., Manchon D., Masmoudi M., Choix des signes pour la formalité de M. Kontsevich, Pacific J. Math.203 (2002) 23-66. Zbl1055.53066MR1895924
- [4] Berezin F., The Method of Second Quantization, Academic Press, New York, 1966. Zbl0151.44001MR208930
- [5] DeWitt B., Supermanifolds, Cambridge Univ. Press, Cambridge, 1992. Zbl0874.53055MR1172996
- [6] Dixmier J., Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. Zbl0308.17007MR498737
- [7] Duflo M., Caractères des algèbres de Lie résolubles, C. R. Acad. Sci.269 (1969) 437-438. Zbl0254.17006MR251089
- [8] Duflo M., Sur les extensions des représentations irréductibles des groupes de Lie nilpotents, Ann. Sci. École Norm. Sup.5 (1972) 71-120. Zbl0241.22030MR302823
- [9] Duflo M., Construction of primitive ideals in an enveloping algebra, in: Gelfand I. (Ed.), Lie Groups and their Representations, Adam Hilger Ltd, London, 1975. Zbl0313.17005MR399194
- [10] Duflo M., Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. École Norm. Sup.10 (1977) 267-288. Zbl0353.22009MR444841
- [11] Duflo M., Rais M., Sur l'analyse harmonique sur les groupes de Lie résolubles, Ann. Sci. École Norm. Sup.9 (1976) 107-114. Zbl0324.43011
- [12] Fulton W., MacPherson R., Compactification of configuration spaces, Ann. Math. (2)139 (1994) 183-225. Zbl0820.14037MR1259368
- [13] Helgason S., The surjectivity of invariant differential operators on a symmetric space, Ann. Math. (2)98 (1973) 451-479. Zbl0274.43013MR367562
- [14] Kashiwara M., Vergne M., The Campbell–Hausdorff formula and invariant hyperfunctions, Invent. Math.47 (1978) 249-272. Zbl0404.22012MR492078
- [15] Kirillov A.A., Merits and demerits of the orbit method, Bull. Amer. Math. Soc.36 (1999) 433-488. Zbl0940.22013MR1701415
- [16] Kontsevich M., private communication.
- [17] Kostant B., Graded Manifolds, Graded Lie Theory and Prequantization, Lect. Notes in Math., 570, Springer, Berlin, 1977. Zbl0358.53024MR580292
- [18] Lewy H., An example of a smooth linear partial differential equation without solution, Ann. Math. (2)66 (1957) 155-158. Zbl0078.08104MR88629
- [19] Manin Yu., Gauge Field Theory and Complex Geometry, Springer, Berlin, 1988. Zbl0641.53001MR954833
- [20] Rais M., Solutions élémentaires des opérateurs différentiels bi-invariants sur un groupe de Lie nilpotent, C. R. Acad. Sci.273 (1971) 495-498. Zbl0236.46047MR289720
- [21] Rais M., Opérateurs différentiels bi-invariants (d'après M. Duflo), Lect. Notes in Math., 667, Springer, Berlin, 1978, pp. 125–137. Zbl0385.22005MR521764
- [22] Shoikhet B., Vanishing of the Kontsevich integral of the wheels, e-print, math.QA/0007080. Zbl1018.53043
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