The stabilized automorphism group of a subshift

2020/01/26 by Hartman, Yair, Kra, Bryna, Schmieding, Scott · 1 citation
#37B10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.09530

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.

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• Stabilized automorphism groups and full groups of odometers

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