Uniqueness theorems for topological higher-rank graph C-algebras

Jean Renault, Aidan Sims, Dana P. Williams, Trent Yeend

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)669-684
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number2
Publication statusPublished - Feb 2018
Externally publishedYes


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