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Cambridge University Press, Bulletin of the Australian Mathematical Society, 1(82), p. 120-138, 2010

DOI: 10.1017/s0004972709001269

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Periodic 2-graphs arising from subshifts

Journal article published in 2010 by David Pask, Iain Raeburn, Natasha A. Weaver ORCID
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This paper is available in a repository.

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Abstract

AbstractHigher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz–Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whoseC*-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we calldomino graphs. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for theC*-algebras of domino graphs.