## 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
Originalsprog Engelsk Transactions of the American Mathematical Society 373 4 2591-2657 0002-9947 https://doi.org/10.1090/tran/7981 Udgivet - 2020

ID: 238589818