Purely infinite C*-algebras arising from crossed products

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

2010-06-07

arxiv.org/abs/1006.1304v3

Mathematics

Operator Algebras

22 pages, revised Remark 2.3 and the comments after Theorem 5.4

Scientific paper

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.

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