Freeness of automaton groups vs boundary dynamics

Daniele D'Angeli, Emanuele Rodaro*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite Schreier graph in the boundary of the enriched dual pointed at some essentially non-trivial point. From these results we derive some consequences from the algebraic, algorithmic and dynamical points of view.

Original languageEnglish
Pages (from-to)115-136
Number of pages22
JournalJournal of algebra
Volume462
DOIs
Publication statusPublished - 15 Sep 2016

Keywords

  • Automaton groups
  • Boundary actions
  • Essentially free actions
  • Schreier graphs

ASJC Scopus subject areas

  • Algebra and Number Theory

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