Characterising residually finite dimensional C*-algebras in dynamical contexts

Adam Skalski (Polish Academy of Sciences)

Thursday 1st June, 2023 16:00-17:00 Maths 311B


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, 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.

Joint work with Tatiana Shulman (University of Gothenburg)

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