245 Altgeld Hall, 12:30-1:30 p.m.

SPECIAL ANALYSIS SEMINAR

Professor A. Van Daele, University of Leuven, Belgium

Locally Compact Quantum Groups

Abstract: In this talk, I plan to give a survey of the development in the operator algebra approach to quantum groups over the last decade. I will start with the compact quantum groups as developed by Woronowicz. A compact quantum group is essentially a Hopf $^*$-algebra with a positive integral. If we no longer assume to have an algebra with identity, we obtain a class of locally compact quantum groups that is self dual (in the sense of Pontryagin duality) and that contains both the compact and discrete quantum groups. This purely algebraic theory served as a model for the general locally compact quantum groups.

I will give precise definitions and compare the different notions that have been studied during this period. I will also discuss some of the examples and how they influenced the final definition of a locally compact quantum group.

A variety of seminars series are being held during Summer 2001. Click for detailed information about dates, times and speakers in these seminar series.