Higher rank graphs, k-subshifts and k-automata
R. Exel, Benjamin Steinberg · arXiv (Cornell University) · 2018
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 $Λ$.