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Automorphisms of Z^d-subshifts of finite type

Ward, T.

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Authors

T. Ward



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

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Accepted Journal Article (215 Kb)
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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Indagationes mathematicae. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Indagationes mathematicae, 5/4, 1994, 10.1016/0019-3577(94)90020-5





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