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Uniqueness theorems for topological higher-rank graph C-algebras

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 u...

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Published in:arXiv.org 2012-09
Main Authors: Renault, Jean N, Sims, Aidan, Williams, Dana P, Yeend, Trent
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Yeend, Trent
description 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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subjects Algebra
Graphs
Topology
Uniqueness theorems
title Uniqueness theorems for topological higher-rank graph C-algebras
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