Boundary actions, germs and quasi-regular representations

Eduardo Scarparo (Federal University of Santa Catarina, Brazil)

Thursday 20th January, 2022 16:00-17:00 Maths 311B


We will present applications of boundary actions to the investigation of the ideal and tracial structure of C*-algebras generated by unitary representations. In particular, for quasi-regular representations associated to stabilizers of boundary actions we have a complete understanding of the trace space of such C*-algebras and when they are simple. We will also show that the groupoid of germs of the action of Thompson's group T on S^1 is non-Hausdorff, and its essential C*-algebra is a possible example of Kirchberg algebra without Cartan subalgebra.

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