Abstract
We prove that ifis a row-finite k-graph with no sources, then the associated C � -algebra is simple if and only ifis 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 ofin terms of ideals in C � (�).
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