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

  title={Simplicity of C*‐algebras associated to higher‐rank graphs},
  author={David I. Robertson and Aidan Sims},
  journal={Bulletin of the London Mathematical Society},
  • D. RobertsonA. Sims
  • Published 7 February 2006
  • Mathematics
  • Bulletin of the London Mathematical Society
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). 

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