TY - JOUR
T1 - Automorphism groups of random substitution subshifts
AU - Fokkink, Robbert
AU - Rust, Dan
AU - Salo, Ville
PY - 2023
Y1 - 2023
N2 - We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.
AB - We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are countable, non-amenable and non-residually finite. To show this, we introduce the concept of shuffles and generalised shuffles for random substitutions, as well as a local version of recognisability for random substitutions that will be of independent interest. Without recognisability, we need a more refined notion of recognisable words in order to understand their automorphisms. We show that the existence of a single recognisable word is often enough to embed the automorphism group of a full shift in the automorphism group of the random substitution subshift.
KW - Amenability
KW - Automorphisms
KW - Random substitutions
KW - Topological conjugacy
UR - http://www.scopus.com/inward/record.url?scp=85171741213&partnerID=8YFLogxK
U2 - 10.1016/j.indag.2023.08.006
DO - 10.1016/j.indag.2023.08.006
M3 - Article
AN - SCOPUS:85171741213
SN - 0019-3577
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
ER -