Operator Algebra Seminar

Abstract: The study of T(A), the simplex of tracial states for a given C*-algebra A, has a long tradition: sometimes we expect T(A) to be small, sometimes very large (the Poulsen simplex). If the algebra in question is the full group C*-algebra of a discrete group G, the problem amounts to understanding all invariant positive definite functions on G. In this talk we will consider a related problem for full C*-algebras of discrete quantum groups, focusing on central tracial states. I will explain this notion, and describe the classification of tracial central states for q-deformations of classical Lie groups and for some families of `free’ quantum groups (for example for quantum orthogonal groups and for quantum permutation groups).

Based on the joint work with Amaury Freslon and Simeng Wang.