Flow equivalence of G-SFTs

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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
Original languageEnglish
JournalTransactions of the American Mathematical Society
Issue number4
Pages (from-to)2591-2657
Publication statusPublished - 2020

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