2011/01/19 by Ben Maloney, Maloney, Ben, Paulette N. Willis +1 · 2 citations
Computer Science · #37B10 #37B15 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Interconnection Networks and Systems #Operator Algebras (math.OA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1101.3795
openalex publication_date 2011/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concept of a 1-coaligned k-graph and prove that the shift maps of a k-graph pairwise *-commute if and only if the k-graph is 1-coaligned. We then prove that for 2-graphs Λ generated from basic data *-commuting shift maps is equivalent to a condition that implies that C^*(Λ) is simple and purely infinite. We then consider full shift spaces and introduce a condition on a block map which ensures the associated sliding block code *-commutes with the shift.