From groups to Hopf algebras: Cohomology and varieties for modules
Connections for Women: Group Representation Theory and Applications February 01, 2018 - February 02, 2018
Location: MSRI: Simons Auditorium
Group cohomology is a powerful tool in group representation theory.
To a group action on a vector space, one associates a geometric object called its support variety that is defined using group cohomology. Hopf algebras generalize groups and include many important classes of algebras such as Lie algebras and quantum groups. The theory of varieties for modules generalizes to Hopf algebras to some extent, but there are many open questions.
In this introductory talk, we will define Hopf algebras, their cohomology, and the corresponding varieties for modules. We will discuss known and unknown properties and recent and current research on open problems
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