Automorphisms of \(\mathbb Z^ d\)-subshifts of finite type
type: Item
instance of: scholarly article
title: Automorphisms of \(\mathbb Z^ d\)-subshifts of finite type
zbMATH Open document ID: 0823.28007
DOI: 10.1016/0019-3577(94)90020-5
author: Thomas B. Ward
published in: Indagationes Mathematicae. New Series
publication date: 1995-10-08T00:00:00Z
review text: Let \((\Sigma, \sigma)\) be a \(\mathbb Z^ d\)-subshift of finite type. The automorphism group \(\Aut(\Sigma)\) is the group of homeomorphisms of \(\Sigma\) commuting with \(\sigma\). This paper extends to dimensions \(d>1\) results of \textit{M. Boyle}, \textit{D. Lind} and \textit{D. Rudolph} [Trans. Am. Math. Soc. 306, No. 1, 71--114 (1988; Zbl 0664.28006)] and Curtis, Hedlund and Lyndon [see \textit{G. A. Hedlund}, Topological Dynamics, Int. Symp. Colorado State Univ. 1967, 259--289 (1968; Zbl 0195.52702)]. In particular, it is shown that under a strong irreducibility condition, \(\Aut(\Sigma)\) contains any finite group. For \(\mathbb Z^ d\)-subshifts of finite type without this irreducibility condition, it is shown using examples that topological mixing is not sufficient to give any finite group in the automorphism group, in general. \(\Aut(\Sigma)\) is explicitly calculated for a particular topological mixing \(\mathbb Z^ 2\)-subshift of finite type and some open questions are posed.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 749795
zbMATH Keywords: subshifts of finite type
zbMATH Keywords: automorphism group
zbMATH Keywords: strong irreducibility condition
zbMATH Keywords: topological mixing
Wikidata QID: Q61835184
reviewed by: Geoffrey R. Goodson
MaRDI profile type: Publication
full work available at URL: 0019-3577(94)90020-5
OpenAlex ID: W1583217685
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description: scientific article; zbMATH DE number 749795