Flow Equivalence of G-SFTs

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.

The paper has been augmented considerably and the second version is now 81 pages long. This version has been accepted for publication in Transactions of the American Mathematical Society

References in corpus (3)

• Flow equivalence of sofic shifts
• Flow equivalence and isotopy for subshifts
• Finite group extensions of shifts of finite type: K-theory, Parry and Livšic