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Uniqueness Theorems For Topological Higher-rank Graph C*-algebras

Journal Article


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Abstract


  • We consider the boundary-path groupoids of topological higher-rank graphs. We show that all such groupoids are topologically amenable. We deduce that the $ C^*$-algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. We then provide a necessary and sufficient condition for simplicity of a topological higher-rank graph $ C^*$-algebra, and a condition under which it is also purely infinite.

Authors


  •   Renault, Jean (external author)
  •   Sims, Aidan D.
  •   Williams, Dana P. (external author)
  •   Yeend, Trent M. (external author)

Publication Date


  • 2018

Citation


  • Renault, J., Sims, A., Williams, D. P. & Yeend, T. (2018). Uniqueness Theorems For Topological Higher-rank Graph C*-algebras. Proceedings Of The American Mathematical Society, 146 (2), 669-684.

Scopus Eid


  • 2-s2.0-85030480607

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1928&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/926

Number Of Pages


  • 15

Start Page


  • 669

End Page


  • 684

Volume


  • 146

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • We consider the boundary-path groupoids of topological higher-rank graphs. We show that all such groupoids are topologically amenable. We deduce that the $ C^*$-algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. We then provide a necessary and sufficient condition for simplicity of a topological higher-rank graph $ C^*$-algebra, and a condition under which it is also purely infinite.

Authors


  •   Renault, Jean (external author)
  •   Sims, Aidan D.
  •   Williams, Dana P. (external author)
  •   Yeend, Trent M. (external author)

Publication Date


  • 2018

Citation


  • Renault, J., Sims, A., Williams, D. P. & Yeend, T. (2018). Uniqueness Theorems For Topological Higher-rank Graph C*-algebras. Proceedings Of The American Mathematical Society, 146 (2), 669-684.

Scopus Eid


  • 2-s2.0-85030480607

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1928&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/926

Number Of Pages


  • 15

Start Page


  • 669

End Page


  • 684

Volume


  • 146

Issue


  • 2

Place Of Publication


  • United States