Labelled space $C^*$-algebras as partial crossed products and a simplicity characterization

TL;DR

This paper establishes an isomorphism between labelled space $C^*$-algebras and partial crossed products, providing a new simplicity criterion and applying it to subshift $C^*$-algebras.

Contribution

It introduces a novel characterization of simplicity for labelled space $C^*$-algebras and links them to partial crossed products.

Findings

Isomorphism between labelled space $C^*$-algebras and partial crossed products

New simplicity characterization for labelled space $C^*$-algebras

Application to $C^*$-algebras of subshifts

Abstract

A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras is given and applied to $C^*$-algebras of subshifts.