Maximal ideals of reduced group C*-algebras and Thompsons groups

Chris Bruce (University of Glasgow)

Thursday 25th April 16:00-17:00 Maths 116

Abstract

I will present on joint work with Kevin Aguyar Brix, Kang Li, and Eduardo Scarparo in which we study maximal ideals in reduced C*-algebras of discrete groups. Our main result reduces the problem of computing maximal ideals in such C*-algebras to the amenable case: Given a fixed point x in the Furstenberg boundary of a group G, we prove that there is a bijection between maximal ideal of the reduced C*-algebra of G and maximal co-induced ideal of the C*-algebra of the stabiliser subgroup of x. As an application, we prove that the reduced C*-algebra of Thompson’s group T has a unique maximal ideal.

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