IMAR 75
Characterising residually finite dimensional $C^*$-algebras in dynamical contexts
Adam Skalski
University of Bucharest and Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
University of Bucharest and Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
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,
and still somewhat mysterious notion appearing in the theory of operator algebras,
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 arising as 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. Based on joint work with Tatiana Shulman (University of Gothenburg).
In this talk I will present certain characterisations of the RFD property for $C^*$-algebras arising as 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. Based on joint work with Tatiana Shulman (University of Gothenburg).