COAMENABILITY OF TYPE-I LOCALLY COMPACT QUANTUM GROUPS VIA CONVOLUTION OPERATORS

We say that a locally compact quantum group is type I if its universal C*-algebra (which is the universal version of the C*-algebra of continuous functions vanishing at infinity on the dual quantum group) is type I. This class of quantum groups can be thought of as an intermediate step between compact and locally compact quantum groups. Type-I locally compact quantum groups are significantly more general than compact quantum groups, but still have tractable representation theory. If G is a compact quantum group, then one can introduce certain convolution operators whose properties allow us to detect whether G is coamenable. The aim of the talk is to outline some results concerning a generalization of this coamenability criterion to the case of type-I locally compact quantum groups.