REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: I will introduce the small quantum group associated to a simple Lie algebra L. This is a finite dimensional Hopf algebra with a number of fantastic properties, from the perspective of conformal field theory and low dimensional topology. (For example, it is factorizable and ribbon.) I will explain how decorations of the Dynkin diagram for L lead to new (non-isomorphic) Hopf algebras with the same fantastic properties. I will also explain how these new Hopf algebras fit into recent studies of non-semisimple tensor categories, and provide us with new examples of tensor equivalences which are not reducible to well-understood semisimple phenomenon. No deep knowledge of Hopf algebras or tensor categories will be assumed, and all basic terminology will be explained.