Gauge-invariant ideals of C*-algebras of Boolean dynamical systems

TL;DR

This paper extends the class of C*-algebras associated with Boolean dynamical systems, proving a gauge-invariant uniqueness theorem and classifying gauge-invariant ideals, thereby broadening understanding of their structure and quotients.

Contribution

It enlarges the class of C*-algebras of Boolean dynamical systems to include all weakly left-resolving normal labelled space C*-algebras and classifies their gauge-invariant ideals.

Findings

Proved a gauge-invariant uniqueness theorem.

Classified all gauge-invariant ideals.

Described quotients as C*-algebras of relative generalized Boolean dynamical systems.

Abstract

We enlarge the class of $C^*$-algebras of Boolean dynamical systems in order to include all weakly left-resolving normal labelled space $C^*$-algebras in it. We prove a gauge-invariant uniqueness theorem and classify all gauge-invariant ideals of these $C^*$-algebras of generalized Boolean dynamical systems and describe the corresponding quotients as $C^*$-algebras of relative generalized Boolean dynamical systems.