Periodic 2-graphs arising from subshifts

Authors

David Pask, University of WollongongFollow
Iain Raeburn, University of WollongongFollow
Natasha A. Weaver, University of Newcastle

RIS ID

33977

Publication Details

Pask, D., Raeburn, I. & Weaver, N. A. (2010). Periodic 2-graphs arising from subshifts. Bulletin of the Australian Mathematical Society, 82 (1), 120-138.

Abstract

Higher-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 whose C 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 call domino 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 the C algebras of domino graphs.