Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

Details Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

2007-08-01

arxiv.org/abs/0708.0245v2

Mathematics

Operator Algebras

18 pages, 1 figure, figure drawn using Tikz/PGF. Version 2: the hypothesis "with no sources" has been removed from Theorem 3.4

Scientific paper

In previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda 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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