An Isaac Newton Institute Workshop

Trends in Noncommutative Geometry

On quantum groups from multiplicative unitaries

Author: Piotr M. Soltan (Department of Mathematical Methods in Physics, Faculty of Physics, Warsaw University)

Abstract

I will describe the theory of quantum groups defined by (modular) multiplicative unitary operators. In this approach to quantum groups we do not assume existence of Haar measures. Moreover there can be many different multiplicative unitaries giving rise to the same quantum group. Nevertheless, I will show that all the important objects of the theory are independent of the choice of the multiplicative unitary operator. The most important of these objects is the ultraweak topology on the C*-algebra describing our quantum group. In classical case this topology determines the class of the Haar measure.