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Automorphisms of Z^d-subshifts of finite type.

Ward, T. (1994) 'Automorphisms of Z^d-subshifts of finite type.', Indagationes mathematicae., 5 (4). pp. 495-504.


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.

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Publisher 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
Record Created:12 Oct 2012 13:20
Last Modified:17 Oct 2012 10:47

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