The Haar measure on locally compact quantum groups
by
Alfons VanDaele
University of Leuven

Locally compact quantum groups have been defined recently by Kustermans and Vaes as pairs (A, \Phi) of a C^*-algebra A and a comultiplication \Phi on A satisfying a relatively simple set of axioms. One of the axioms is the existence of a (nice) left and right Haar measure. Up to now, it has not been possible (in the general case) to formulate reasonable axioms from which the existence of the Haar measures can be proven.

In this talk, I will begin with recalling the definition of a locally compact quantum group. Then I will focus on a certain type of examples (introduced by Woronowicz) and show how the Haar measure can be obtained for these examples. Finally, I will draw some conclusions about the general theory of locally compact quantum groups and the possibility to obtain a framework where the existence of the Haar measure is no longer part of the set of axioms, but a theorem.

Date received: June 19, 2000