Flow equivalence of G-SFTs

Boyle, Mike; Carlsen, Toke; Eilers, Søren

doi:10.1090/tran/7981

Flow equivalence of G-SFTs
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Trans. Amer. Math. Soc. 373 (2020), 2591-2657 Request permission

Abstract:

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.

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