On one-sided topological conjugacy of topological Markov shifts and gauge actions on Cuntz--Krieger algebras

TL;DR

This paper characterizes when one-sided topological Markov shifts are topologically conjugate by examining the associated Cuntz--Krieger algebras and their gauge actions with potentials, linking dynamical systems and operator algebras.

Contribution

It provides a new characterization of topological conjugacy classes of one-sided topological Markov shifts using Cuntz--Krieger algebras and gauge actions.

Findings

Topological conjugacy classes are characterized via Cuntz--Krieger algebras.

Gauge actions with potentials are key to understanding conjugacy.

The approach bridges dynamical systems and operator algebra theory.

Abstract

We will characterize topological conjugacy classes of one-sided topological Markov shifts in terms of the associated Cuntz--Krieger algebras and its gauge actions with potentials.