The automorphism group of a shift of slow growth is amenable

Van Cyr, Bryna Kra

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose is a subshift, is the word complexity function of, and is the group of automorphisms of. We show that if, then is amenable (as a countable, discrete group). We further show that if, then can never contain a non-abelian free monoid (and, in particular, can never contain a non-abelian free subgroup). This is in contrast to recent examples, due to Salo and Schraudner, of subshifts with quadratic complexity that do contain such a monoid.

Original languageEnglish (US)
Pages (from-to)1788-1804
Number of pages17
JournalErgodic Theory and Dynamical Systems
Volume40
Issue number7
DOIs
StatePublished - Jul 1 2020

Keywords

  • Subshift
  • amenable
  • automorphism
  • block complexity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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