The stabilized automorphism group of a subshift

Yair Hartman, Bryna Kra, Scott Schmieding

Research output: Working paper/PreprintPreprint

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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.
Original languageEnglish GB
StatePublished - 2020

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Dynamical Systems
  • 37B10

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