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Journal of Operator Theory

Volume 86, Issue 2, Fall 2021  pp. 395-424.

Orbit equivalence of higher-rank graphs

Authors:  Toke Meier Carlsen (1), James Rout (2)
Author institution:(1) Department of Science and Technology, University of the Faroe Islands, Vestara Bryggja 15, FO-100 Torshavn, Faroe Islands
(2) School of Mathematics and Statistics, University of New South Wales, Kensington, NSW 2052, Australia

Summary: We study the notion of continuous orbit equivalence of finitely-aligned higher-rank graphs. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic. We also study eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs.

Keywords: higher-rank graph, orbit equivalence, conjugacy, multi-dimensional shift space, groupoid, $k$-graph $C^*$-algebra, Kumjian-Pask algebra

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