Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 335-347.

Simplicity of finitely aligned $k$-graph $C^\ast$-algebras

Authors: Jacob Shotwell
Author institution: Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85281, U.S.A.

Summary: It is shown that \textit{no local periodicity} is equivalent to the \textit{aperiodicity condition} for arbitrary finitely aligned $k$-graphs. This allows us to conclude that $C^\ast(\Lambda)$ is simple if and only if $\Lambda$ is cofinal and has no local periodicity.

Keywords: $k$-graph, $C^*$-algebra, graph algebra

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