Purely infinite C*-algebras arising from crossed products

TY - JOUR

T1 - Purely infinite C*-algebras arising from crossed products

AU - Rørdam, Mikael

AU - Sierakowski, Adam

PY - 2012/2

Y1 - 2012/2

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0143-3857

VL - 32

SP - 273

EP - 293

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

ER -