One-sided topological conjugacy of normal subshifts and gauge actions on the associated $C^*$-algebras

TL;DR

This paper characterizes when two normal subshifts are topologically conjugate by examining the associated $C^*$-algebras and their gauge actions, providing a new algebraic perspective on symbolic dynamics.

Contribution

It introduces a characterization of one-sided topological conjugacy of normal subshifts using $C^*$-algebras and gauge actions, extending the understanding of their algebraic invariants.

Findings

Normal subshifts are characterized by their $C^*$-algebras and gauge actions.

The paper establishes a correspondence between topological conjugacy and algebraic isomorphisms.

It covers a broad class of subshifts including Markov, sofic, and Dyck shifts.

Abstract

The class of normal subshifts includes irreducible infinite topological Markov shifts, irreducible infinite sofic shifts, synchronized systems, Dyck shifts, $\beta$-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated $C^*$-algebras and its gauge actions with potentials.