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Simplicity of C*-algebras associated to higher-rank graphs

Journal Article


Abstract


  • We prove that if \Lambda is a row-finite k-graph with no sources, then the associated C*-algebra is simple if and only if \Lambda is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as Condition (A). We prove that the aperiodicity condition is equivalent to a suitably modified version of Robertson and Steger's original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinality and aperiodicity of \Lambda in terms of ideals in C*(\Lambda).

UOW Authors


  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2007

Citation


  • Robertson, D. I. & Sims, A. D. (2007). Simplicity of C*-algebras associated to higher-rank graphs. Bulletin of the London Mathematical Society, 39 (2), 337-344.

Scopus Eid


  • 2-s2.0-39149135162

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3018

Number Of Pages


  • 7

Start Page


  • 337

End Page


  • 344

Volume


  • 39

Issue


  • 2

Place Of Publication


  • http://blms.oxfordjournals.org/archive/

Abstract


  • We prove that if \Lambda is a row-finite k-graph with no sources, then the associated C*-algebra is simple if and only if \Lambda is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as Condition (A). We prove that the aperiodicity condition is equivalent to a suitably modified version of Robertson and Steger's original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinality and aperiodicity of \Lambda in terms of ideals in C*(\Lambda).

UOW Authors


  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2007

Citation


  • Robertson, D. I. & Sims, A. D. (2007). Simplicity of C*-algebras associated to higher-rank graphs. Bulletin of the London Mathematical Society, 39 (2), 337-344.

Scopus Eid


  • 2-s2.0-39149135162

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3018

Number Of Pages


  • 7

Start Page


  • 337

End Page


  • 344

Volume


  • 39

Issue


  • 2

Place Of Publication


  • http://blms.oxfordjournals.org/archive/