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Purely infinite C-algebras arising from crossed products

Journal Article


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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.

Publication Date


  • 2012

Citation


  • Rordam, M. & Sierakowski, A. (2012). Purely infinite C-algebras arising from crossed products. Ergodic Theory and Dynamical Systems, 32 (1), 273-293.

Scopus Eid


  • 2-s2.0-84655162286

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1569&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/563

Number Of Pages


  • 20

Start Page


  • 273

End Page


  • 293

Volume


  • 32

Issue


  • 1

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.

Publication Date


  • 2012

Citation


  • Rordam, M. & Sierakowski, A. (2012). Purely infinite C-algebras arising from crossed products. Ergodic Theory and Dynamical Systems, 32 (1), 273-293.

Scopus Eid


  • 2-s2.0-84655162286

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1569&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/563

Number Of Pages


  • 20

Start Page


  • 273

End Page


  • 293

Volume


  • 32

Issue


  • 1