Deformation quantization and invariant differential operators

Panagiotis Batakidis

doi:10.1016/j.crma.2010.11.007

Lie Algebras/Harmonic Analysis

Deformation quantization and invariant differential operators

Presented by: Michel Duflo

Panagiotis Batakidis ¹

¹ Department of Mathematics, Aristotle University of Thessaloniki, Konstantinou Karamanli, Panepistimioupoli, 54124 Thessaloniki, Greece

Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 143-148.

Abstract
Résumé

In this Note we explain how the techniques of deformation quantization in the sense of Kontsevich can be used to describe the algebra of invariant differential operators on Lie groups.

Nous expliquons dans cette Note comment les méthodes de quantification par déformation, au sens de Kontsevich, peuvent être utilisées pour décrire l'algèbre des opérateurs différentiels invariants sur un groupe de Lie.

Received: 2010-09-16
Accepted: 2010-11-09
Published online: 2011-01-06

DOI: 10.1016/j.crma.2010.11.007

Author's affiliations:

Panagiotis Batakidis ¹

¹ Department of Mathematics, Aristotle University of Thessaloniki, Konstantinou Karamanli, Panepistimioupoli, 54124 Thessaloniki, Greece

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     author = {Panagiotis Batakidis},
     title = {Deformation quantization and invariant differential operators},
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     pages = {143--148},
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     language = {en},
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Panagiotis Batakidis. Deformation quantization and invariant differential operators. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 143-148. doi : 10.1016/j.crma.2010.11.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.007/

References
Cited by

[1] P. Batakidis, Déformation par quantification et théorie de Lie, thèse de doctorat, Univ. Paris VII, 2009.

[2] A.S. Cattaneo; G. Felder Coisotropic submanifolds in Poisson geometry and branes in the Poisson Sigma model, Lett. Math. Phys., Volume 69 (2004), pp. 157-175

[3] A.S. Cattaneo; G. Felder Relative formality theorem and quantization of coisotropic submanifolds, Adv. Math., Volume 208 (2007) no. 2, pp. 521-548

[4] A.S. Cattaneo; B. Keller; Ch. Torossian; A. Bruguieres Déformation, Quantization, Théorie de Lie, Collection Panoramas et Synthèse, vol. 20, SMF, 2005

[5] A.S. Cattaneo; Ch. Torossian Quantification pour les paires symmétriques et diagrammes de Kontsevich, Ann. Sci. Ec. Norm. Super. (5) (2008), pp. 787-852

[6] M. Kontsevich Deformation quantization of Poisson manifolds, Lett. Math. Phys., Volume 66 (2003) no. 3, pp. 157-216

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