Algebras of one-sided subshifts over arbitrary alphabets
Rings and Algebras
2023-12-04 v2 Dynamical Systems
Operator Algebras
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 as a partial skew group ring.
Cite
@article{arxiv.2211.02148,
title = {Algebras of one-sided subshifts over arbitrary alphabets},
author = {Giuliano Boava and Gilles G. de Castro and Daniel Gonçalves and Daniel W. van Wyk},
journal= {arXiv preprint arXiv:2211.02148},
year = {2023}
}
Comments
40 pages