Published January 2005
by Societe Mathematique de France .
Written in English
|The Physical Object|
Home» MAA Publications» MAA Reviews» Déformation, Quantification, Théorie de Lie Déformation, Quantification, Théorie de Lie Alberto Cattaneo, Bernhard Keller, Charles Torossian, and Alain Bruguières. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain. Unfortunately, there is no real textbook on DQ around. One has Fedosov's book on his construction of star products including a detailed exposition of his index theorem. There is a chapter on DQ in the recent Poisson geometry book . This article in French, with a large English introduction, is a survey about applications of bi-quantization theory in Lie theory. We focus on a conjecture of M. Duflo. Most of the applications are coming from our article with Alberto Cattaneo [Cattaneo, A.S., Torossian, C.: Quantification pour les paires symétriques et diagrammes de Cited by: 3.
Book "Déformation, Quantification, Théorie de Lie," (Panoramas et Synthèses, n°20, ) Book "Higher Structures in Geometry and Physics," (Birkhäuser, ). Higher Structures, Zurich University, November , Poisson Geometry Home Page Some theses in my group Internal lecture notes. Applications de la bi-quantification à la théorie de Lie quantification, théorie de Lie. he also opened up new research avenues in Lie theory, quantum group theory, deformation theory Author: Charles Torossian. In Torossian (J Lie Theory 12(2)–, ), the second author used the Kontsevich deformation quantization technique to define a natural connection ω . M. Flato, A. Lichnerowicz, D. Sternheimer, Déformations 1-différentiales des algèbres de Lie attachées à une variété symplectique ou de contact. Compositio Math. 31, 47–82 () zbMATH MathSciNet Google ScholarAuthor: Chiara Esposito.
Concerning the path integral approach to deformation quantization (work of Cattaneo--Felder), that is mentionned in Bertram Arnold's comment, Kontsevich's approach relies on a Sigma model with 2d source/worldsheet (the so-called Poisson sigma-model), while Fedosov's procedure can be unerstood as relying on a sigma model with 1d source. CONTACT MAA. Mathematical Association of America 18th Street NW Washington, D.C. Phone: () - Phone: () - Fax: () - Buy Représentations et Quantification: Représentations des groupes de Lie conformes et Quantification des espaces symétriques () (French Edition) on FREE SHIPPING on qualified orders. Bernhard Keller is the author of Touchpoint Management - inkl. Arbeitshilfen online ( avg rating, 1 rating, 0 reviews), Marktforschung für die Smart 4/5(1).