Flow equivalence of G-SFTs

In this paper, a G-shift of finite type ( G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over th...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2020-04, Vol.373 (4), p.2591-2657
Main Authors: Boyle, Mike, Carlsen, Toke, Eilers, Søren
Format: Article
Language:English
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Summary:In this paper, a G-shift of finite type ( G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G. For a special case of two irreducible components with G=\mathbb{Z}_2, we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G-SFT applications, including a new connection to involutions of cellular automata.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7981