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Bimodules and branes in deformation quantization

Part of: Groups and algebras in quantum theory Homological methods

Published online by Cambridge University Press:  11 August 2010

Damien Calaque ,
Giovanni Felder ,
Andrea Ferrario  and
Carlo A. Rossi
Damien Calaque
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France (email: calaque@math.univ-lyon1.fr)
Giovanni Felder
Affiliation:
Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland (email: giovanni.felder@math.ethz.ch)
Andrea Ferrario
Affiliation:
Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland (email: andrea.ferrario@math.ethz.ch)
Carlo A. Rossi
Affiliation:
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal (email: crossi@math.ist.utl.pt)
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Abstract

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We prove a version of Kontsevich’s formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X*) and ∧(X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet’s recent paper on Koszul duality in deformation quantization.

Keywords

deformation quantizationcoisotropic submanifoldsKoszul algebrasKoszul dualityL∞-algebras and morphismsA∞-bimodules

MSC classification

Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16E45: Differential graded algebras and applications 81R60: Noncommutative geometry

Information

Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 105 - 160
Copyright
Copyright © Foundation Compositio Mathematica 2010

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