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Deformation Quantization and Reduction

Alberto S. Cattaneo
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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 L-infinity and A-infinity 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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Alberto S. Cattaneo. 2007-06-11. Deformation Quantization and Reduction. https://doi.org/10.5167/uzh-6703

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