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

Abstract

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

28 pages. Version 2 is a slightly revised version of version 1, and is the version that was published in Journal of Mathematical Analysis and Applications. In version 2 (and the published version), there were some small mistakes on page 24 and in the proof of Lemma 7.2.(2) on page 25. They have been corrected in version 3 (see also https://doi.org/10.1016/j.jmaa.2020.124754)

References in corpus (4)

• Adding tails to C*-correspondences
• C*-algebras of labelled graphs
• Ideal structure of $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences
• The structure of gauge-invariant ideals of labelled graph $C^{\ast }$-algebras

Cited by in corpus (2)

• Condition (K) for Boolean dynamical systems
• The simplicity of the C*-algebras associated to arbitrary labeled spaces