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

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Bulletin of the London Mathematical Society, Vol: 39, Issue: 2, Page: 337-344

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Robertson, David I; Sims, Aidan
era2012; era2010
article description
We prove that if Λ is a row-finite k-graph with no sources, then the associated C*-algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask’s aperiodicity condition, known as Condition (A). We prove that the aperiodicity condition 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 Λ in terms of ideals in C∗(Λ).