Freeness of automaton groups vs boundary dynamics

Daniele D'Angeli, Emanuele Rodaro

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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.

Originalspracheenglisch
Seiten (von - bis)115-136
Seitenumfang22
FachzeitschriftJournal of algebra
Jahrgang462
DOIs
PublikationsstatusVeröffentlicht - 15 Sep 2016

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Transducer
Automata
Finite Graph
Semigroup
Class

Schlagwörter

    ASJC Scopus subject areas

    • !!Algebra and Number Theory

    Dies zitieren

    Freeness of automaton groups vs boundary dynamics. / D'Angeli, Daniele; Rodaro, Emanuele.

    in: Journal of algebra, Jahrgang 462, 15.09.2016, S. 115-136.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    D'Angeli, Daniele ; Rodaro, Emanuele. / Freeness of automaton groups vs boundary dynamics. in: Journal of algebra. 2016 ; Jahrgang 462. S. 115-136.
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