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Purely infinite partial crossed products

Journal Article


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Abstract


  • Let (A,G,α)(A,G,α) be a partial dynamical system. We show that there is a bijective correspondence between G -invariant ideals of AA and ideals in the partial crossed product A⋊α,rGA⋊α,rG provided the action is exact and residually topologically free. Assuming, in addition, a technical condition—automatic when AA is abelian—we show that A⋊α,rGA⋊α,rG is purely infinite if and only if the positive nonzero elements in AA are properly infinite in A⋊α,rGA⋊α,rG. As an application we verify pure infiniteness of various partial crossed products, including realisations of the Cuntz algebras OnOn, OAOA, ONON, and OZOZ as partial crossed products.

Publication Date


  • 2014

Citation


  • Giordano, T. & Sierakowski, A. (2014). Purely infinite partial crossed products. Journal of Functional Analysis, 266 (9), 5733-5764.

Scopus Eid


  • 2-s2.0-84897066365

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3234&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2225

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 5733

End Page


  • 5764

Volume


  • 266

Issue


  • 9

Place Of Publication


  • United States

Abstract


  • Let (A,G,α)(A,G,α) be a partial dynamical system. We show that there is a bijective correspondence between G -invariant ideals of AA and ideals in the partial crossed product A⋊α,rGA⋊α,rG provided the action is exact and residually topologically free. Assuming, in addition, a technical condition—automatic when AA is abelian—we show that A⋊α,rGA⋊α,rG is purely infinite if and only if the positive nonzero elements in AA are properly infinite in A⋊α,rGA⋊α,rG. As an application we verify pure infiniteness of various partial crossed products, including realisations of the Cuntz algebras OnOn, OAOA, ONON, and OZOZ as partial crossed products.

Publication Date


  • 2014

Citation


  • Giordano, T. & Sierakowski, A. (2014). Purely infinite partial crossed products. Journal of Functional Analysis, 266 (9), 5733-5764.

Scopus Eid


  • 2-s2.0-84897066365

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3234&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2225

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 5733

End Page


  • 5764

Volume


  • 266

Issue


  • 9

Place Of Publication


  • United States