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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.

Keywords: topological $k$-graph, higher-rank graph, graph algebra, aperiodicity

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