Flow equivalence of G-SFTs
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- by Mike Boyle, Toke Meier Carlsen and Søren Eilers PDF
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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.References
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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
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 2591-2657
- MSC (2010): Primary 37B10; Secondary 37A35
- DOI: https://doi.org/10.1090/tran/7981
- MathSciNet review: 4069229