表示论研讨班：Support variety theory for finite dimensional algebras

数学研究所

学术报告

表示论研讨班

Speaker: 陈一萍 教授（武汉大学）

Title: Support variety theory for finite dimensional algebras
   

Time&Venue: 2024年11月12日（星期二）11:00-12:00 & 思源楼S817
   

Abstract: Support is a fundamental concept to provide a geometric approach for studying

 all kinds of algebraic structure. Based on Quillen's work, the description of the algebraic

 varieties corresponding to the cohomology ring of a finite group, Carlson introduced a

 support variety of any finitely generated module over a finite group G whose dimension

 is given by the complexity of the module. The support variety of a module is a powerful 

invariant in the modular representation theory of a finite group, and contains a lot of deep 

structure information about modular representations of finite groups. The very active

 direction in this field is to develop and generalize the theory of support varieties to finite 

dimensional algebras (due to Snashall and Solberg), and read off homological information 

on the module itself.  This needs a non-trivial assumption which is known as the (Fg) condition. 

(Fg 1) There exists a noetherian graded subring H of the Hochschild cohomology ring HH(A).

(Fg 2) The Yoneda algebra Ext(X,Y) is a finitely generated H-module for all A-modules X

 and Y. In this talk, we will give a new approach to support varieties. As applications, 

we will show that all skew-gentle algebras satisfy the (Fg) condition, and the support 

variety of any indecomposable module over a skew-gentle algebra is point or a curve.

 It follows that the complexity of any module over a skew-gentle algebra is at most one. 

This is a joint work with Steffen Koenig.