PhD Thesis Defence

Benjamin Anderson-Sackaney, Department of Pure Mathematics, University of Waterloo

"Amenability Properties and Subobjects of Quantum Groups"

We will discuss a structural result for the left ideals of quantum group algebras of compact quantum groups. Then, we will discuss a duality result between relative amenability and co-amenability of certain coideals of a compact quantum group G and its (discrete) dual. This latter result is used to establish a characterization of the unique trace property of the reduced C*-algebra C_r(G), and that simplicity of C_r(G) implies the unique trace property for Kac G. In the general case, we achieve an existence result for tracial states on C_r(G).

MC 2009