2006/02/28 by David I. Robertson, Aidan Sims · 1 citation
Mathematics · #math.OA #msc:46L05
paper · pdf · doi:10.1112/blms/bdm006
published as D.I. Robertson and A. Sims, 'Simplicity of C*-algebras associated to higher-rank graphs,' Bull. London Math. Soc., 39 (2007), no. 2, 337--344 · 9 pages, 1 figure. Numbering of environments and enumeration style changed to match published version. Author contact details updated
arxiv created 2007/12/12 · arxiv updated 2009/12/01
We prove that if Λis a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if Λis cofinal and satisfies Kumjian and Pask's Condition (A). We prove that Condition (A) 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 Λin terms of ideals in C^*(Λ).