Uniqueness property for $C^*$-algebras given by relations with circular symmetry

TL;DR

This paper presents a unified method to analyze the uniqueness property of $C^*$-algebras with circle gauge actions, connecting various isomorphism theorems and the Cuntz-Krieger uniqueness theorem.

Contribution

It introduces a general approach that unifies the understanding of the uniqueness property across different classes of $C^*$-algebras with circular symmetry.

Findings

Unified framework for $C^*$-algebra uniqueness properties

Connections between crossed product isomorphisms and Cuntz-Krieger theorems

Applicable to a broad class of $C^*$-algebras with circle actions

Abstract

A general method of investigation of the uniqueness property for $C^*$-algebra equipped with a circle gauge action is discussed. It unifies isomorphism theorems for various crossed products and Cuntz-Krieger uniqueness theorem for Cuntz-Krieger algebras.