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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Flow equivalence of G-SFTs
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by Mike Boyle, Toke Meier Carlsen and Søren Eilers PDF
Trans. Amer. Math. Soc. 373 (2020), 2591-2657 Request permission

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
  • © 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