OpAlg seminar: Andreas Aaserud

Abstract: Starting from an object in a braided C*-tensor category, one gets non-commutative AF-algebras whose K-theory has a natural commutative (ordered) ring structure. We show that, in special cases, this K-ring is isomorphic to the fusion ring of the initial category, or of a subcategory, or to the quotient of a polynomial ring. I will focus on the category of positive energy loop group representations of SU(2) at level k, which can also be described using Temperley-Lieb diagrams. Our computations are based on earlier work of Erlijman-Wenzl, Evans-Gould, D. Handelman, V. Jones, L. Kauffman, A. Wassermann, and others.

This is joint work with Professor David E. Evans at Cardiff University. Motivated by the Freed-Hopkins-Teleman theorem, which realizes some of the aforementioned fusion rings using twisted equivariant K-theory, our long-term goal is to obtain a simpler K-theoretical construction of the fusion rings, and to realize the underlying tensor category via modules over a suitable C*-algebra.