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Transactions of the American Mathematical Society

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Flow equivalence of G-SFTs


Authors: Mike Boyle, Toke Meier Carlsen and Søren Eilers
Journal: Trans. Amer. Math. Soc. 373 (2020), 2591-2657
MSC (2010): Primary 37B10; Secondary 37A35
DOI: https://doi.org/10.1090/tran/7981
Published electronically: January 7, 2020
MathSciNet review: 4069229
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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.


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Additional Information

Mike Boyle
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
MR Author ID: 207061
ORCID: 0000-0003-0050-0542
Email: mmb@math.umd.edu

Toke Meier Carlsen
Affiliation: Department of Science and Technology, University of the Faroe Islands, Vestara Bryggja 15, FO-100 Tórshavn, The Faroe Islands
MR Author ID: 685180
ORCID: 0000-0002-7981-7130
Email: toke.carlsen@gmail.com

Søren Eilers
Affiliation: Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
MR Author ID: 609837
Email: eilers@math.ku.dk

Received by editor(s): March 10, 2016
Received by editor(s) in revised form: May 4, 2019, and August 16, 2019
Published electronically: January 7, 2020
Article copyright: © Copyright 2019 American Mathematical Society