The stabilized automorphism group of a subshift
Dynamical Systems
2020-01-28 v1
Abstract
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group, study its algebraic properties, and use them to distinguish many of the stabilized automorphism groups. We also show that for a full shift, the subgroup of the stabilized automorphism group generated by elements of finite order is simple, and that the stabilized automorphism group is an extension of a free abelian group of finite rank by this simple group.
Cite
@article{arxiv.2001.09530,
title = {The stabilized automorphism group of a subshift},
author = {Yair Hartman and Bryna Kra and Scott Schmieding},
journal= {arXiv preprint arXiv:2001.09530},
year = {2020}
}
Comments
55 pages