SFT covers for actions of the first Grigorchuk group
: Grigorchuk, Rostislav; Salo, Ville
: Bezushchak, O.; Drozd, Yu.; Etingof, P.; Futorny, V.; Grigorchuk, R.; Zelmanov, E.
: Ukraine Algebraic Conference
Publisher: American Mathematical Society
: 2025
Contemporary Mathematics
: Modern Algebra Volume 2: Groups and Algebras
: 830
: 127
: 158
: 978-1-4704-7619-9
: 0271-4132
: 1098-3627
DOI: https://doi.org/10.1090/conm/830/16562
: https://doi.org/10.1090/conm/830/16562
: https://research.utu.fi/converis/portal/detail/Publication/523322406
: https://arxiv.org/abs/2403.06480
We study symbolic dynamical representations of actions of the first Grigorchuk group G, namely its action on the boundary of the infinite rooted binary tree, its representation in the topological full group of a minimal substitutive Z-shift, and its representation as a minimal system of Schreier graphs. We show that the first system admits an SFT cover, and the latter two systems are conjugate to sofic subshifts on G, but are not of finite type.
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The first author is supported by the Humboldt Foundation, and expresses his gratitude to the University of Bielefeld. Also, he is supported by the Travel Support for Mathematicians grant MP-TSM-00002045 from the Simons Foundation.
