Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs
arXiv:0708.0245
Abstract
In previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λwith no sources is simple if and only if Λis 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.
arXiv comment18 pages, 1 figure, figure drawn using Tikz/PGF. Version 2: the hypothesis "with no sources" has been removed from Theorem 3.4; it appeared there in error since the main point of the theorem is that it applies in the absence of this hypothesis (cf Theorem 3.1 of arXiv:math/0602120)