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Support varieties for Hopf algebras

Banff International Research Station for Mathematical Innovation and Discovery

Support varieties are a tool providing some information about representations. They were first introduced by Quillen for finite groups, and have since been generalized in several directions, including to finite dimensional self-injective algebras (under some finiteness assumptions). One asks which properties of support varieties for finite group representations are true more generally? In this talk, we will give an overview of the theory of varieties for modules of self-injective algebras. We will focus on the tensor product property for Hopf algebras, that is, that the variety of a tensor product of modules is the intersection of the varieties. We will give examples of Hopf algebras constructed from finite groups for which the tensor product property does not hold.

Mathematics; Associative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: Texas A&M University

2017-03-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60880

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/