Séminaire Physique mathématique ICJ

Towards an HKR-Theorem for Coisotropic Reduction

by Dr Marvin Dippell (Salerno)

Fokko du Cloux (Bâtiment Braconnier)

Fokko du Cloux (Bâtiment Braconnier)


Deformation quantization aims at constructing a quantum mechanical analogue to a given classical mechanical system by (formally) deforming the commutative algebra of functions on a given Poisson manifold (M,pi) into a non-commutative algebra describing the associated quantum system. In this talk I will present a general framework for incorporating the additional information of a coisotropic submanifold C in M into its algebra of functions and study the deformation theory of these so-called constraint algebras. I will present some first results towards a constraint Hochschild-Kostant-Rosenberg Theorem and in particular compute the second contraint Hochschild cohomology in the case of R^n.