Modules and morphisms in deformation quantization: old and new
Speaker:Prof. Martin Bordemann, Université de Haute Alsace
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
We shall deal with the simultaneous deformation of associative algebras and their (bi)modules applied to deformation quantization on smooth manifolds. There is an obvious formulation in terms of differential graded Lie algebras already mentioned by D.Arnal et al in 1983. We discuss two particular cases: 1. the space of smooth functions on a submanifold (which has to be coisotropic due to Gabber's Theorem), 2. the space of of smooth fonctions on the total space of a fibered manifold over a Poisson manifold. In both cases we compute the corresponding cohomologies (in terms of differential Hochschild cohomology), related this to the differential geometry (e.g. adapted poly-vectorfields), and discuss L-infinity formality. This is joint work with Benedikt HURLE, Mulhouse.
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