Abstract
In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.
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Robertson, D., Sims, A. Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs. Isr. J. Math. 172, 171–192 (2009). https://doi.org/10.1007/s11856-009-0070-5
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DOI: https://doi.org/10.1007/s11856-009-0070-5