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Deformation quantization and reduction


Cattaneo, A S (2008). Deformation quantization and reduction. In: Dito, G. Poisson geometry in mathematics and physics : international conference, June 5 - 9, 2006, Tokyo, Japan. Providence, RI, US: American Mathematical Society , 79-101.

Abstract

This note is an overview of the Poisson sigma model (PSM) and
its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L1- and A1-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson–Lie groups.

Abstract

This note is an overview of the Poisson sigma model (PSM) and
its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L1- and A1-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson–Lie groups.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:13 Jan 2009 15:58
Last Modified:05 Apr 2016 12:38
Publisher:American Mathematical Society
Series Name:Contemporary mathematics
Number:450
ISSN:0271-4132
ISBN:978-0-8218-4423-6
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2397620
http://opac.nebis.ch/F/?local_base=NEBIS&con_lng=GER&func=find-b&find_code=SYS&request=005577000

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