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Purely infinite C*-algebras arising from crossed products

Published online by Cambridge University Press:  05 April 2011

MIKAEL RØRDAM  and
ADAM SIERAKOWSKI
MIKAEL RØRDAM
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark (email: [email protected])
ADAM SIERAKOWSKI
Affiliation:
The Fields Institute for Research in Mathematical Sciences, 222 College Street, Second Floor, Toronto, Canada M5T 3J1 (email: [email protected], [email protected]) Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada M3J 1P3
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 273 - 293
Copyright
Copyright © Cambridge University Press 2011

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