Groups and Operator Algebras Seminar

Speaker: Adam Skalski (IMPAN)

Title: Characterising residually finite dimensional C*-algebras in dynamical contexts

Abstract: A C*-algebra is said to be residually finite-dimensional (RFD) when it has 'sufficiently many' finite-dimensional representations. The RFD property is an important, natural, and still somewhat mysterious notion, admitting several equivalent descriptions and having subtle connections to residual finiteness properties of groups. In this talk I will present certain characterisations of the RFD property for C*-algebras of amenable étale groupoids and for C*-algebraic crossed products by amenable actions of discrete groups, extending (and inspired by) earlier results of Bekka, Exel and Loring. I will also explain the role of the amenability assumption and describe several consequences of our main theorems. Finally I will discuss some examples, notably these related to semidirect products of groups, and outstanding open problems. Based on the joint work with Tatiana Shulman.

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