Journal of Operator Theory

Volume 72, Issue 1, Summer 2014 pp. 3-14.

Aperiodicity conditions in topological

$k$ -graphs

Authors: Sarah E. Wright
Author institution: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, 01610, U.S.A.

Summary: We give two new conditions on topological

$k$ -graphs equivalent to Yeend's aperiodicity condition

$A$ . Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new construction of a twisted topological

$k$ -graph, to demonstrate the improvements achieved by the new conditions. Reducing this proof of equivalence to the discrete case also gives a new direct proof of the corresponding conditions in discrete

$k$ -graphs, where previous proofs depended on simplicity of the corresponding

$C^*$ -algebra.

DOI: http://dx.doi.org/10.7900/jot.2012aug20.196
Keywords: topological

$k$ -graph, higher-rank graph, graph algebra, aperiodicity

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