Groups and Dynamics Seminar

Date: February 22, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Constantine Medynets, US Naval Academy

Title: Characters of Countable Groups and Ergodic Properties of Their Actions

Abstract: In the 1980s Vershik observed that given an extreme character chi -- satisfying certain conditions -- of the infinite symmetric group S(N) there is an ergodic action of S(N) on a standard measure (X,mu) such that chi(g)=mu(Fix(g)), where Fix(g) is the set of fixed points of the group element g. In this talk, we will discuss two classes of groups where extreme characters can be uniquely described as measures of fixed points of ergodic actions similarly to Vershik’s construction above. We will discuss the class of Higman-Thompson’s groups and the class of AF full groups associated with simple Bratteli diagrams. Note that in view of the Gelfand-Naimark-Segal construction the classification of characters is equivalent to the classification of the finite type von Neumann algebra representations of the group in question.