题目：From Algebraic Groups to Finite Dimensional Algebras

报告人：王建磐（华东师范大学）

时间：2013年1月16日（周三）14:50-15:50

地点：数学系（致远楼）107

摘要:

The study of quasi-hereditary algebras has been a hot topic for about two decades in the circle of finite dimensional algebras. Interestingly, the notion of such algebras is first introduced by mathematicians working on algebraic groups, instead of those working on finite dimensional algebras.

My talk will focus on why this happened. Thus, I shall explore the source of the theory of quasi-hereditary algebras in the representation theory of algebraic groups. That is, I shall show how highest weight categories appear naturally in representation theory of algebraic groups, leading to the definition of quasi-hereditary algebras.

This is a good example showing that different branches of mathematics may have some common intrinsic kernels, which make the branches connect to each other. It also shows that creations sometimes occur in certain fields closed to your research interests, instead of your research field itself.

As a concrete example of bridges connecting the theory of algebraic groups and that of finite dimensional algebras, Schur algebras from different views, together of their quantization and certain further generalizations, will also be exhibited.