University of Georgia
Mathematics Department Colloquium
Shuzhou Wang
February 1 1999
Simple compact quantum groups
ABSTRACT: In the mid-80's, Woronowicz introduced the general notion
of compact quantum groups. He and Soibelman-Vaksman independently
constructed the first non-trivial examples of such objects by the
method of deformation of simple compact Lie groups, which are also
called the compact real forms of the Drinfeld-Jimbo quantum groups.
Later, starting with his Ph.D. thesis, the speaker and his
collaborators discovered and studied several new classes
of compact quantum groups of a completely different nature.
Meanwhile, it has been an outstanding problem to find an appropriate
notion of simple compact quantum groups. In this talk, we will propose
a definition of simple compact quantum groups and show that the examples
mentioned above are simple compact quantum groups. We will also
discuss the problem of classifying simple compact quantum groups.