It is a classical result that the simple algebras in the category of finite dimensional vector spaces are precisely the n x n matrix algebras. The notion of algebras in more general tensor categories is easy to formulate, and we can ask for classification results in these categories. Such classification results have broad applications to conformal field theory, topological quantum field theory, and subfactor theory. In this talk I will present some progress on the classification of algebras in the categories coming from the quantum groups of type A. In particular I will show the existence of a new family of exceptional examples.

Location: Jointly in person and virtually on Zoom (speaker will be remote). SAS 4201 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at cmjones6@ncsu.edu to be added.