TY - JOUR

T1 - Flow equivalence of G-SFTs

AU - Boyle, Mike

AU - Carlsen, Toke Meier

AU - Eilers, Soren

PY - 2020

Y1 - 2020

N2 - 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

AB - 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

U2 - 10.1090/tran/7981

DO - 10.1090/tran/7981

M3 - Journal article

VL - 373

SP - 2591

EP - 2657

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 4

ER -