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The ideal structure of reduced crossed products

Journal Article


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Abstract


  • Let (A, G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular

    we determine sufficient—and in some cases also necessary—conditions for A to separate

    the ideals in A ⋊r G. When A separates the ideals in A ⋊r G, then there is a one-to-one

    correspondence between the ideals in A ⋊r G and the invariant ideals in A. We extend

    the concept of topological freeness and present a generalization of the Rokhlin property.

    Exactness properties of (A, G) turns out to be crucial in these investigations.

Publication Date


  • 2010

Citation


  • Sierakowski, A. (2010). The ideal structure of reduced crossed products. Munster Journal of Mathematics, 3 237-262.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1900&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/894

Number Of Pages


  • 25

Start Page


  • 237

End Page


  • 262

Volume


  • 3

Place Of Publication


  • http://miami.uni-muenster.de/servlets/DerivateServlet/Derivate-6174/mjm_vol_3_13.pdf

Abstract


  • Let (A, G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular

    we determine sufficient—and in some cases also necessary—conditions for A to separate

    the ideals in A ⋊r G. When A separates the ideals in A ⋊r G, then there is a one-to-one

    correspondence between the ideals in A ⋊r G and the invariant ideals in A. We extend

    the concept of topological freeness and present a generalization of the Rokhlin property.

    Exactness properties of (A, G) turns out to be crucial in these investigations.

Publication Date


  • 2010

Citation


  • Sierakowski, A. (2010). The ideal structure of reduced crossed products. Munster Journal of Mathematics, 3 237-262.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1900&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/894

Number Of Pages


  • 25

Start Page


  • 237

End Page


  • 262

Volume


  • 3

Place Of Publication


  • http://miami.uni-muenster.de/servlets/DerivateServlet/Derivate-6174/mjm_vol_3_13.pdf