报告题目: Deformation quantization ofalgebras 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 ofdeformation quantization is to find for a given a Poisson manifold X a starproduct which deforms the Poisson bracket. A star product is a non-commutativeassociative product on the algebra of formal power series of smooth functionson the manifold X, such that the zeroth order is given by the usual product offunctions and the antisymmetric part of the first order in the formal parameteris given by the given Poisson bracket. This has essentially been solved byKontsevich and others. In this talk we will consider the situation of asurjective submersion or fibre bundle. In this case the functions on the totalspace can be seen as a module over the functions on the base. We want to givecriteria when it is possible to deform this module structure as module orbimodule. To do so I introduce first the describing differential gradedLie 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 asbimodule there are obstructions in general.

报告人简介：Benedikt Hurle 陈省身数学所博士后