Algebras of one-sided subshifts over arbitrary alphabets
Giuliano Boava
Universidade Federal de Santa Catarina, Florianópolis Sc, BrazilGilles G. de Castro
Universidade Federal de Santa Catarina, Florianópolis Sc, BrazilDaniel Gonçalves
Universidade Federal de Santa Catarina, Florianópolis-Sc, BrazilDaniel W. van Wyk
Fairfield University, USA; University of the Free State, Bloemfontein, South Africa
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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