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.
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.
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.
| 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: | 01 Dec 2023 02:47 |
| Publisher: | American Mathematical Society |
| Series Name: | Contemporary mathematics |
| Number: | 450 |
| ISSN: | 0271-4132 |
| ISBN: | 978-0-8218-4423-6 |
| OA Status: | Green |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2397620 |
Cattaneo, A S