C*-irreducible inclusions of commensurated subgroups

Eduardo Scarparo (Universidade Federal de Pelotas)

Thursday 12th October, 2023 16:00-17:00 Maths 311B


An inclusion of groups H < G is said to be C*-irreducible if any intermediate C*-algebra between (and including) the reduced C*-algebras of H and G is simple. We will present a complete characterization of C*-irreducible inclusions coming from commensurated subgroups in terms of dynamical and group theoretical properties. As an application, we will see that PSL(n,Z) < PSL(n,Q) is a C*-irreducible inclusion, and that the inclusion of any C*-simple group into its abstract commensurator is C*-irreducible. We will also discuss some examples beyond commensurated subgroups which still lack an explanatory theory. This is based on joint work with Kang Li.

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