Document Type
Journal Article
RIS ID
20303
Citation
Robertson, David I. and Sims, Aidan, 2007, Simplicity of C*-algebras associated to higher-rank graphs, Bulletin of the London Mathematical Society, 39(2), 337-344.
http://ro.uow.edu.au/era/413
Abstract
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).
COinS