Automorphisms of Z^d-subshifts of finite type

Ward, T.

Abstract

Let (S,s) be a Z^d-subshift of finite type. Under a strong irreducibility condition (strong specification), we show that Aut(S) contains any finite group. For Z^d-subshifts of finite type without strong specification, examples show that topological mixing is not sufficient to give any finite group in the automorphism group in general: in particular, End(S) may be an abelian semigroup. For an example of a topologically mixing Z^2-subshift of finite type, the endomorphism semigroup and automorphism group are computed explicitly. This subshift has periodic-point permutations that do not extend to automorphisms.

Citation

Ward, T. (1994). Automorphisms of Z^d-subshifts of finite type. Indagationes Mathematicae, 5(4), 495-504. https://doi.org/10.1016/0019-3577%2894%2990020-5

• Journal Article Type: Article
• Publication Date: Jan 1, 1994
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Oct 17, 2012
• Journal: Indagationes Mathematicae
• Print ISSN: 0019-3577
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: 4
• Pages: 495-504
• DOI: https://doi.org/10.1016/0019-3577%2894%2990020-5
• Public URL: https://durham-repository.worktribe.com/output/1502367