Non-commutative integration on quantum groups

July 19th, 2011, Departemental seminar (UNSW, Sydney).

Abstract

Quantum groups can be considered as deformations of a function algebra on locally compact groups. Many properties of abstract harmonic analysis have a suitable interpretation in the deformed setting. For deformations of Lie groups also geometrical properties can be recovered. In this talk, I will give an introduction to quantum groups in an operator algebraic fashion. We will see how Fourier transforms can be defined on the non-commutative L^p-spaces associated with a quantum group.