2010/06/07 by Rordam, Mikael, Sierakowski, Adam · 1 citation
#46L05 #46L35 #46L55 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1006.1304
We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C*-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C*-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C*-algebra is a Kirchberg algebra in the UCT class.