Date:	Fri, March 22, 2013
Time:	11:15
Place:	East Hall 8

Abstract: Given a Lie algebra g, one of the tools in the study of simple g-modules is passing to the enveloping algebra Ug. Since two simple modules cannot be isomorphic if they have different annihilators, one might be interested in understanding the structure of annihilators of the simple Ug-modules. In this talk we will introduce results for the case of semi-simple finite-dimensional Lie algebra g and try to explain how situation changes in case of locally finite infinite-dimensional Lie algebra gl(∞). In case of gl(∞), the investigation of the annihilators of the simple objects in the category of tensor modules ("the closest" analogue of finite-dimensional simple modules) leads to the following main result: two simple tensor modules are isomorphic if and only if they have the same annihilator.