JournalsrmiVol. 40, No. 3pp. 1045–1088

Algebras of one-sided subshifts over arbitrary alphabets

  • Giuliano Boava

    Universidade Federal de Santa Catarina, Florianópolis Sc, Brazil

  • Gilles G. de Castro

    Universidade Federal de Santa Catarina, Florianópolis Sc, Brazil

  • Daniel Gonçalves

    Universidade Federal de Santa Catarina, Florianópolis-Sc, Brazil

  • Daniel W. van Wyk

    Fairfield University, USA; University of the Free State, Bloemfontein, South Africa
Algebras of one-sided subshifts over arbitrary alphabets cover
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Abstract

We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital, and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott–Tomforde–Willis subshifts in terms of a homeomorphism between the Stone duals of suitable Boolean algebras, and in terms of a diagonal-preserving isomorphism of the associated unital algebras. For this, we realise the unital algebra associated with a subshift as a groupoid algebra and a partial skew group ring.

Cite this article

Giuliano Boava, Gilles G. de Castro, Daniel Gonçalves, Daniel W. van Wyk, Algebras of one-sided subshifts over arbitrary alphabets. Rev. Mat. Iberoam. 40 (2024), no. 3, pp. 1045–1088

DOI 10.4171/RMI/1457