Noncommutative Geometry and Topology in Prague

Weak Expectations of Discrete Quantum Group Algebras and Crossed Products

Studying various finite-dimensional approximation properties such as nuclearity, exactness has become one of the central areas of investigation in the theory of C*-algebras. One of the natural questions is whether standard constructions of C*-algebras preserve the approximation properties. In the classical discrete group case, all approximation properties such as nuclearity, weak expectation property of the group C*-algebra can be characterized by the amenability of the group. In this talk, I will present the connection between weak expectations of the discrete quantum group C*-algebras, the crossed product of C*-algebras, and the amenability of the discrete quantum groups. This is joint work with Angshuman Bhattacharya