English

Normal amenable subgroups of the automorphism group of the full shift

Dynamical Systems 2019-03-27 v2

Abstract

We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's Theorem and of the fact that these groups contain free groups.

Keywords

Cite

@article{arxiv.1512.00587,
  title  = {Normal amenable subgroups of the automorphism group of the full shift},
  author = {Joshua Frisch and Tomer Schlank and Omer Tamuz},
  journal= {arXiv preprint arXiv:1512.00587},
  year   = {2019}
}