21 March 2016, 16:00 - 17:00, in HG00.310
Makato Yamashita (Ochanomizu University)
Random walk on monoidal categories and classification of compact quantum groups
Motivated by Izumi's noncommutative Poisson boundary for
discrete quantum groups, we define the notion of categorical Poisson
boundary for C*-tensor categories with duality and irreducible unit.
Motivated by subfactor theory we show that this construction has a
universality property for the amenable tensor functors. As an
application, we obtain a classification result which implies that any
compact quantum group with noninvolutive antipode and the same
combinatorial data of representations as SU(n) essentially arises as a
strict quantization for a Poisson-Lie group structure on SU(n).
This talk is based on joint work with S. Neshveyev.