Speaker: Makoto Yamashita (Ochanomizu Univ.)
Title: Poisson boundary of monoidal categories
Time/Date: 4:30-6:00, Wed. May 28, 2014
Abstract: 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. Such categories naturally appear in the study of subfactors and quantum groups, and we recover many known constructions as a part of this categorical boundary. We prove that the Poisson boundary has a universality property for the amenable dimension function, which clarifies the conceptual meanings behind a result of Hayashi and Yamagami, and a one by Tomatsu. As an application, we obtain that the 2-cohomology of discrete dual does not change when one passes from a coamenable compact quantum group to its maximal Kac quantum subgroup. This talk is based on joint work with S. Neshveyev.