Abstract:
Consider a minimal and free action of a discrete amenable group on a compact metrizable space. The corresponding crossed product $C^*$-algebra is a simple unital separable stably finite $C^*$-algebra, and in the talk I will focus on the structure of this $C^*$-algebra. In particular, I will talk about the classifiability and radius of comparison in terms of the mean dimension of the dynamical system, and I will also talk about the stable rank of this $C^*$-algebra.