Dan Ursu, Pure Mathematics, University of Waterloo
"C*-simplicity of discrete groups"
For every (discrete) group, the canonical C*-algebra associated to this group is the C*-algebra generated by the image of the group under the left-regular representation, known as the reduced group C*-algebra. Of interest here is knowing the fundamental property of when this C*-algebra is simple - that is, it admits no nontrivial closed two-sided ideals. Groups satisfying this property are known as C*-simple, and are in some sense the opposite of amenable groups. Recently, a dynamical characterization of C*-simplicity was obtained by Kalantar and Kennedy, and shortly afterwards an intrinsic (group-theoretic) characterization was obtained by Kennedy as a corollary. In this talk, I will give an overview of these characterizations, and use them to give easy proofs of the C*-simplicity of various groups.
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