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

Authors

Jean Renault, Universite d'Orleans, France
Aidan Sims, University of WollongongFollow
Dana P. Williams, Dartmouth CollegeFollow
Trent M. Yeend, University of NewcastleFollow

RIS ID

117961

Publication Details

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.

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.

Grant Number

ARC/DP120100389