Cris Negron, Massachusetts Institute of Technology
Tuesday, March 28, 2017 - 1:30pm
PDL C-36
Pre-seminar
When: Tuesday March 28, 1:30--2:15
Title: Hopf algebras for beginners
Seminar
When: Tuesday March 28, 2:30--3:20
Title: Small Quantum Groups Associated to Belavin-Drinfeld Triples
Abstract: I will introduce the small quantum group associated to a simple Lie algebra L. This is a finite dimensional Hopf algebra introduced by Lusztig in the 90’s. Small quantum groups have a number of fantastic properties, from the perspective of conformal field theory and low dimensional topology. (For example, they 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 alge- bras 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.
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