Normal amenable subgroups of the automorphism group of the full shift

TL;DR

The paper proves that all normal amenable subgroups of the automorphism group of the full shift are central, using Furstenberg boundaries and extending the result to higher dimensions, also providing new proofs of known theorems.

Contribution

It establishes a new characterization of normal amenable subgroups in automorphism groups of full shifts and extends the results to higher dimensions.

Findings

Normal amenable subgroups are contained in the center

Extension of results to higher-dimensional shifts

Provides new proofs of Ryan's Theorem and free group existence

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.