Finite dimensional Hopf algebras and invariant theory

Algebra / Topology Seminar

Speaker: Ehud Meir

Abstract: 
In this talk I will present an approach to study finite dimensional semisimple Hopf algebras, based on invariant theory.

I will explain why the isomorphism type of such an algebra can be determined by a (very big) collection of invariant scalars, and will discuss the intuitive meaning of these scalars. 

While in some cases they can be very easily interpreted, in some other cases their meaning is much less clear.

I will explain the connection between these invariants and questions about fields of definition, some open problems in Hopf algebra theory (about the dimension of irreducible representations) and how one can use them in order to prove that every such algebra satisfies a certain finiteness condition (the existence of at most finitely many Hopf orders).