Algebra and Combinatorics Seminar

Date: February 8, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Sarah Witherspoon, TAMU

Title: Hopf algebras and the cohomological finite generation conjecture

Abstract: A powerful tool for understanding representations of finite groups is group cohomology. One reason why it is so powerful is that the group cohomology ring is finitely generated and graded commutative, thus pointing to geometric methods. Hopf algebras generalize groups and include many important classes of algebras such as Lie algebras and quantum groups. Their cohomology rings are known to be graded commutative, and it is conjectured that they are finitely generated whenever the Hopf algebra is finite dimensional.

In this introductory talk, we will define Hopf algebras, their cohomology rings, and mention their uses in representation theory. We will discuss Hopf algebras for which the conjecture has been proven and those for which it has not, including recent and ongoing research.