Groupoid models for the C*-algebras of topological higher-rank graphs

Abstract

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on essential freeness and amenability of the groupoids which capture the existing theory, and extend results involving group crossed products of graph algebras.

References in corpus (1)

• Product systems of graphs and the Toeplitz algebras of higher-rank graphs

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• Semigroupoid C*-Algebras
• Product-system models for twisted $C^{\ast }$-algebras of topological higher-rank graphs
• KMS states on the Toeplitz algebras of higher-rank graphs
• Orbit equivalence of higher-rank graphs
• Sheaves of Measures and KMS-Weights on Topological Graph Algebras
• Semigroups of local homeomorphisms and interaction groups