Flow equivalence of G-SFTs
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Flow equivalence of G-SFTs. / Boyle, Mike; Carlsen, Toke Meier; Eilers, Soren.
I: Transactions of the American Mathematical Society, Bind 373, Nr. 4, 2020, s. 2591-2657.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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 -
ID: 238589818