Title: On the Quantum Subgroups generated by Lévy Processes on Compact Quantum Groups
Speaker: Uwe Franz（Laboratoire de Mathématiques de Besançon）
Time: 8.12 (Wednesday), 15:00-14:00
Venue: Gewu Building, Room 315
Abstract: I will give an introduction to the theory of Lévy processes with values in compact quantum groups. Schürmann’s Lévy processes on bialgebras or Hopf algebras and Woronowicz’ compact quantum groups are natural noncommutative (or quantum) generalisations of stochastic processes with sta- tionary and independent increments and compact groups. Combining these two theories allows to apply ideas from probability to the study of the noncommutative geometric structure of quantum groups. Using the notion of Gaussian Lévy processes due to Schürmann we have given a new defi- nition of the connected component of the identity of a compact quantum groups. More generally, we investigate the smallest closed subgroup which can be reached ζcontinuously’ from a fixed sub- group, which we call its Schürmann envelope. I will present our results on these Gaussian parts and Schürmann envelopes, and conclude with several open problems.
