Periodic 2-graphs arising from subshifts

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 $C^{\ast }$-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 \emph{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 $C^{\ast }$-algebras of domino graphs.

17 pages

References in corpus (2)

• Simplicity of C*-algebras associated to higher-rank graphs
• Periodicity in Rank 2 Graph Algebras

Cited by in corpus (5)

• $C^{\ast }$-algebras associated with textile dynamical systems
• $C^{\ast }$-algebras and Fell bundles associated to a textile system
• Cuntz-Krieger algebras associated with Hilbert $C^{\ast }$-quad modules of commuting matrices
• C*-algebras associated with Hilbert C*-quad modules of finite type
• C*-algebras associated with Hilbert C*-quad modules of C*-textile dynamical systems