Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Modular symmetry of Poisson manifolds and the Van den Bergh duality

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 J.-L. 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. This is a work in progress so I will propose a conjecture and give supporting evidence.