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Modular symmetry of Poisson manifolds and the Van den Bergh duality

Le : 10/11/2006 14h15
Par : Vassily DOLGUSHEV (Northeastern University, Chicago et ETH, Zurich)
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Résumé : To a Poisson manifold one can assign the so-called modular class which is an intrinsic element in the space of Poisson vector fields modulo Hamiltonian vector fields. This class was independently introduced and studied by JL Brylinski, A. Weinstein and G. Zuckerman. In my talk I would like to show that the quantum incarnation of the modular class is related to the Van den Bergh duality between Hochschild cohomology and Hochschild homology of the corresponding deformation quantization algebra.