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

Abstract

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

Theorems & Definitions (55)

• Definition 3.1
• Remark 3.2
• Proposition 3.3
• Proposition 3.4
• proof
• Corollary 3.5
• proof
• Remark 3.6
• Proposition 3.7
• proof