Kirchberg's Factorization Property, Residual Finiteness, and Property (T) for Discrete Quantum Groups

Shuzhou Wang  (University of Georgia)

10:00-11:00, March 29, 2019   Science Building A510

Abstract:

In 1964, Takesaki discovered that the product representation of the left and right regular representations of the reduced group C*-algebra of the free group on two generators is unbounded under the minimal/spatial tensor product, thus introducing non-nuclear C*-algebras. Wassermann subsequently showed that the product representation of the left and right regular representation of the full group C*-algebra of the same group is bounded under the minimal/spatial tensor product. Using these ideas, Kirchberg introduced the notion of factorization property for discrete groups and showed that residual finite groups has the factorization property and conversely, groups with both the factorization property and property (T) are residually finite. In this talk, we will explain how to extend these results of Kirberberg for discrete groups to discrete quantum groups and show that the discrete duals of the universal orthogonal and unitary quantum groups have the factorization property when the dimension of the fundamental representation of the latter is different from 3. (Joint work Angshuman Bhattacharya, Michael Brannan, Alexandru Chirvasitu)