Journal of Operator Theory

Volume 57, Issue 1, Winter 2007 pp. 95-120.

Groupoi d models for the $C^*$-algebras of topological higher-rank graphs

Authors: Trent Yeend
Author institution: School of Mathematical & Physical Sciences, University of Newcastle, NSW, 2308, Australia

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

Keywords: Topological graph, higher rank graph, groupoid, graph algebra, Cuntz-Krieger alg ebra.

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