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
Original language | English |
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Journal | Transactions of the American Mathematical Society |
Volume | 373 |
Issue number | 4 |
Pages (from-to) | 2591-2657 |
ISSN | 0002-9947 |
DOIs | |
Publication status | Published - 2020 |