Algebras of one-sided subshifts over arbitrary alphabets

Giuliano Boava ^[1] ; Gilles G. de Castro ^[1] ; Daniel Gonçalves ^[1] ; Daniel W. van Wyk ^[2]
1. [1] Universidade Federal de Santa Catarina
  
  Universidade Federal de Santa Catarina
  
  Brasil
2. [2] University of the Free State
  
  University of the Free State
  
  Mangaung, Sudáfrica
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 1045-1088
Idioma: inglés
DOI: 10.4171/RMI/1457
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Resumen
- 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.