• DOI:10.1112/blms/bdm006
• Corpus ID: 14087459

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

@article{Robertson2006SimplicityOC,
  title={Simplicity of C*‐algebras associated to higher‐rank graphs},
  author={David I. Robertson and Aidan Sims},
  journal={Bulletin of the London Mathematical Society},
  year={2006},
  volume={39}
}

• D. Robertson, A. 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).