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

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...

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Veröffentlicht in:	Journal of mathematical analysis and applications 2020-08, Vol.488 (1), p.124037, Article 124037
Hauptverfasser:	Carlsen, Toke Meier, Kang, Eun Ji
Format:	Artikel
Sprache:	eng
Schlagworte:	[formula omitted]-algebras of Boolean dynamical systems Cuntz-Pimsner algebras Gauge-invariant ideals Gauge-invariant uniqueness theorem Labelled graph [formula omitted]-algebras Relative Cuntz-Pimsner algebras
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Beschreibung
Zusammenfassung:	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.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2020.124037