Algebras of one-sided subshifts over arbitrary alphabets

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.