Aperiodicity Conditions in Topological $k$-Graphs

Details Aperiodicity Conditions in Topological $k$-Graphs Aperiodicity Conditions in Topological $k$-Graphs

2011-10-18

arxiv.org/abs/1110.4026v1

Mathematics

Operator Algebras

12 pages, 3 figures

Scientific paper

We give two new conditions on topological $k$-graphs that are equivalent to the 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.

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