Simplicity of C*-algebras associated to higher-rank graphs

Abstract

We prove that if Λis a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if Λis cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) is equivalent to a suitably modified version of Robertson and Steger's original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinality and aperiodicity of Λin terms of ideals in C^*(Λ).

9 pages, 1 figure. Numbering of environments and enumeration style changed to match published version. Author contact details updated

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• A family of 2-graphs arising from two-dimensional subshifts
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• Two families of Exel-Larsen crossed products
• Endomorphisms and Modular Theory of 2-Graph C*-Algebras