THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY

By Van Cyr, Bryna Kra. Forum of Mathematics, Sigma, 2014

65 citations recorded by the source corpus.

For a finite alphabet ${\mathcal{A}}$ and shift $X\subseteq {\mathcal{A}}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group $\text{Aut}(X)$. For such systems, we show that every finitely generated subgroup of $\text{Aut}(X)$ is virtually $\mathbb{Z}^{d}$, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if $X$ is transitive, then $\text{Aut}(X)$ is virtually $\mathbb{Z}$; if $X$ has dense aperiodic points, then $\text{Aut}(X)$ is virtually $\mathbb{Z}^{d}$. We also classify all finite groups that arise as the automorphism group of a shift.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/734b464f0d28cf8daa00068c51ac625c8c7a027c

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Citations in the corpus

The automorphism group of a minimal shift of stretched exponential growth (2015, background): “Over the past several years, the authors [4, 5] and others (e.”
On automorphism groups of low complexity subshifts (2015, methodology): “In the process of submitting this article, we became aware of a new article by Cyr and Kra [12].”