报告题目: Deformation quantization of algebras and modules

报 告 人：Benedikt Hurle 陈省身数学所博士后

报告时间：3月22日 3：00-3：50

报告地点：数学楼 617

报告摘要:

The original problem of deformation quantization is to find for a given a Poisson manifold X a star product which deforms the Poisson bracket. A star product is a non-commutative associative product on the algebra of formal power series of smooth functions on the manifold X, such that the zeroth order is given by the usual product of functions and the antisymmetric part of the first order in the formal parameter is given by the given Poisson bracket. This has essentially been solved by Kontsevich and others. In this talk we will consider the situation of a surjective submersion or fibre bundle. In this case the functions on the total space can be seen as a module over the functions on the base. We want to give criteria when it is possible to deform this module structure as module or bimodule.  To do so I introduce first the describing differential graded Lie algebra and cohomology for the deformation of an algebra and (bi)module. For the situation considered, this cohomology can be computed. This proves e.g. that the deformation as module is always possible while for the deformation as bimodule there are obstructions in general.

报告人简介：Benedikt Hurle 陈省身数学所博士后