C*-Algebras of one-sided subshifts over arbitrary alphabets

Abstract

We associate a C*-algebra ${\tilde{\mathcal{O}}}_{\text{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that ${\tilde{\mathcal{O}}}_{\text{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that ${\tilde{\mathcal{O}}}_{\text{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that ${\tilde{\mathcal{O}}}_{\text{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of ${\tilde{\mathcal{O}}}_{\text{X}}$ and illustrate it with two examples.