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arXiv · 1512.05238

Flow Equivalence of G-SFTs

Mike Boyle·Toke Meier Carlsen·Søren Eilers
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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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Mike Boyle, Toke Meier Carlsen, Søren Eilers. 2019-08-26. Flow Equivalence of G-SFTs. https://doi.org/10.1090/tran%2F7981

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