Title: Compact Quantum Groups and their Semidirect Products
by Sutanu Roy (National Institute of Science Education and Research) as part of Topological Groups
Lecture held in Elysium.
Compact quantum groups are noncommutative analogs of compact groups in the realm of noncommutative geometry introduced by S. L. Woronowicz back in the 80s. Roughly, they are unital C*-bialgebras in the monoidal category (given by the minimal tensor product) of unital C*-algebras with some additional properties. For real 0<|q|<1, q-deformations of SU(2) group are the first and well-studied examples of compact quantum groups. These examples were constructed independently by Vaksman-Soibelman and Woronowicz also back in the 80s. In fact, they are examples of a particular class of compact quantum groups namely, compact matrix pseudogroups. The primary goal of this talk is to motivate and discuss some of the interesting aspects of this theory from the perspective of the compact groups. In the second part, I shall briefly discuss the semidirect product construction for compact quantum groups via an explicit example. The second part of this will be based on a joint work with Paweł Kasprzak, Ralf Meyer and Stanislaw Lech Woronowicz.