Higher rank graphs, k-subshifts and k-automata

2018/09/13 by R. Exel, Exel, R., Benjamin Steinberg +1
Computer Science · Mathematics · #46L05 #46L55 #Advanced Operator Algebra Research #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1809.04932

openalex publication_date 2018/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a k-graph Λ we construct a Markov space M_Λ, and a collection of k pairwise commuting cellular automata on M_Λ, providing for a factorization of Markov's shift. Iterating these maps we obtain an action of \mathbb N^k on M_Λ which is then used to form a semidirect product groupoid M_Λ\rtimes \mathbb N^k. This groupoid turns out to be identical to the path groupoid constructed by Kumjian and Pask, and hence its C*-algebra is isomorphic to the higher rank graph C*-algebra of Λ.

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