Uniqueness theorems for topological higher-rank graph C*-algebras

@article{Renault2009UniquenessTF,
  title={Uniqueness theorems for topological higher-rank graph C*-algebras},
  author={Jean N. Renault and Aidan Sims and Dana P. Williams and Trent Yeend},
  journal={arXiv: Operator Algebras},
  year={2009}
}
We consider the boundary-path groupoids of topological higher-rank graphs. We show that the 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. 
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