I will give an overview of properties of amenable groups, as well as of the lesser known classes of supramenable groups (introduced by Rosenblatt in 1974), respectively, groups with the fixed point property for cones (recently introduced by Monod), with emphasis on how these groups act on C*-algebras. It is, for example, well-known that any action of an amenable group on a unital C*-algebra with a tracial state admits at least one invariant trace, while any non-amenable group can act on, say, the Cantor set, such that the crossed product is purely infinite and simple (and hence traceless). We consider similar statements for actions of groups on non-unital C*-algebras, which are more subtle, and turn out to involve the above classes of supramenable groups and groups with the fixed point property for cones.
Department of Mathematical Sciences, University of Copenhagen
Thu, 14/02/2019 - 12:00pm
RC-4082, The Red Centre, UNSW