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On twisted higher-rank graph C*-algebras

Journal Article


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Abstract


  • We define the categorical cohomology of a k-graph Λ and show

    that the first three terms in this cohomology are isomorphic to the corresponding

    terms in the cohomology defined in our previous paper. This leads to

    an alternative characterisation of the twisted k-graph C∗-algebras introduced

    there. We prove a gauge-invariant uniqueness theorem and use it to show

    that every twisted k-graph C∗-algebra is isomorphic to a twisted groupoid

    C∗-algebra. We deduce criteria for simplicity, prove a Cuntz-Krieger uniqueness

    theorem and establish that all twisted k-graph C∗-algebras are nuclear

    and belong to the bootstrap class.

Publication Date


  • 2015

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2015). On twisted higher-rank graph C*-algebras. Transactions of the American Mathematical Society, 367 (7), 5177-5216.

Scopus Eid


  • 2-s2.0-84927652118

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9709&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2373

Has Global Citation Frequency


Number Of Pages


  • 39

Start Page


  • 5177

End Page


  • 5216

Volume


  • 367

Issue


  • 7

Place Of Publication


  • United States

Abstract


  • We define the categorical cohomology of a k-graph Λ and show

    that the first three terms in this cohomology are isomorphic to the corresponding

    terms in the cohomology defined in our previous paper. This leads to

    an alternative characterisation of the twisted k-graph C∗-algebras introduced

    there. We prove a gauge-invariant uniqueness theorem and use it to show

    that every twisted k-graph C∗-algebra is isomorphic to a twisted groupoid

    C∗-algebra. We deduce criteria for simplicity, prove a Cuntz-Krieger uniqueness

    theorem and establish that all twisted k-graph C∗-algebras are nuclear

    and belong to the bootstrap class.

Publication Date


  • 2015

Citation


  • Kumjian, A., Pask, D. & Sims, A. (2015). On twisted higher-rank graph C*-algebras. Transactions of the American Mathematical Society, 367 (7), 5177-5216.

Scopus Eid


  • 2-s2.0-84927652118

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9709&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2373

Has Global Citation Frequency


Number Of Pages


  • 39

Start Page


  • 5177

End Page


  • 5216

Volume


  • 367

Issue


  • 7

Place Of Publication


  • United States