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

We prove that if ᴧ is a row-fiuit e k-graph with no sources, then the associated C*-algebra is simple if and only if ᴧ 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 modifi ed 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 ᴧ in terms of ideals in C* (ᴧ).