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Twisted C∗-algebras associated to finitely aligned higher-rank graphs

Journal Article


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Abstract


  • We introduce twisted relative Cuntz-Krieger algebras associated

    to finitely aligned higher-rank graphs and give a comprehensive

    treatment of their fundamental structural properties. We establish

    versions of the usual uniqueness theorems and the classification

    of gauge-invariant ideals. We show that all twisted relative Cuntz-

    Krieger algebras associated to finitely aligned higher-rank graphs are

    nuclear and satisfy the UCT, and that for twists that lift to real-valued

    cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is

    independent of the twist. In the final section, we identify a sufficient

    condition for simplicity of twisted Cuntz-Krieger algebras associated

    to higher-rank graphs which are not aperiodic. Our results indicate

    that this question is significantly more complicated than in the untwisted

    setting.

UOW Authors


  •   Sims, Aidan
  •   Whitehead, Benjamin (external author)
  •   Whittaker, Michael F. (external author)

Publication Date


  • 2014

Citation


  • Sims, A., Whitehead, B. & Whittaker, M. F. (2014). Twisted C∗-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19 831-866.

Scopus Eid


  • 2-s2.0-84920178066

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3762&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2753

Has Global Citation Frequency


Number Of Pages


  • 35

Start Page


  • 831

End Page


  • 866

Volume


  • 19

Place Of Publication


  • Germany

Abstract


  • We introduce twisted relative Cuntz-Krieger algebras associated

    to finitely aligned higher-rank graphs and give a comprehensive

    treatment of their fundamental structural properties. We establish

    versions of the usual uniqueness theorems and the classification

    of gauge-invariant ideals. We show that all twisted relative Cuntz-

    Krieger algebras associated to finitely aligned higher-rank graphs are

    nuclear and satisfy the UCT, and that for twists that lift to real-valued

    cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is

    independent of the twist. In the final section, we identify a sufficient

    condition for simplicity of twisted Cuntz-Krieger algebras associated

    to higher-rank graphs which are not aperiodic. Our results indicate

    that this question is significantly more complicated than in the untwisted

    setting.

UOW Authors


  •   Sims, Aidan
  •   Whitehead, Benjamin (external author)
  •   Whittaker, Michael F. (external author)

Publication Date


  • 2014

Citation


  • Sims, A., Whitehead, B. & Whittaker, M. F. (2014). Twisted C∗-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19 831-866.

Scopus Eid


  • 2-s2.0-84920178066

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3762&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2753

Has Global Citation Frequency


Number Of Pages


  • 35

Start Page


  • 831

End Page


  • 866

Volume


  • 19

Place Of Publication


  • Germany