Simple algebras in Rep(uq(sl2))

Abstract: The notion of an algebra in a tensor category plays an important role in the theory of tensor categories and their applications. Simple algebras in finite tensor categories, much like in ordinary ring theory, form one of the most fundamental classes of algebras. Although simple algebras are especially important in Morita theory of finite tensor categories, the basic theory of simple algebras is not yet fully developed. In this talk, I will present some Morita theoretic results on module categories over finite tensor categories and explain how these results can be applied to construct simple algebras with additional properties, such as being Frobenius or symmetric Frobenius. I will also present examples in the category Rep(uq(sl2)) of modules over the small quantum sl2 at a root of unity of odd order. This talk is based on joint work with Daisuke Nakamura, Hin Wan Ng and Taiki Shibata.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home