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

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

2006-02-07

arxiv.org/abs/math/0602120v2

D.I. Robertson and A. Sims, 'Simplicity of C*-algebras associated to higher-rank graphs,' Bull. London Math. Soc., 39 (2007),

Mathematics

Operator Algebras

9 pages, 1 figure. Numbering of environments and enumeration style changed to match published version. Author contact details

Scientific paper

10.1112/blms/bdm006

We prove that if \Lambda is a row-finite k-graph with no sources, then the associated C^*-algebra is simple if and only if \Lambda is 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 \Lambda in terms of ideals in C^*(\Lambda).

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