C∗-algebras of generalized Boolean dynamical systems as partial crossed products

In this paper, we realize C ∗ -algebras of generalized Boolean dynamical systems as partial crossed products. Reciprocally, we give some sufficient conditions for a partial crossed product to be isomorphic to a C ∗ -algebra of a generalized Boolean dynamical system. As an application, we show that g...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 58; no. 2; pp. 355 - 385
Main Authors de Castro, Gilles G., Kang, Eun Ji
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2023
Springer Nature B.V
Subjects
Boolean algebra
Combinatorics
Computer Science
Convex and Discrete Geometry
Dynamical systems
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Secondary: 37B99
Partial crossed products
Graded ideals
Partial actions
algebras
Primary: 46L55
46L05
Gauge-invariant ideals
Generalized Boolean dynamical systems
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Summary:In this paper, we realize C ∗ -algebras of generalized Boolean dynamical systems as partial crossed products. Reciprocally, we give some sufficient conditions for a partial crossed product to be isomorphic to a C ∗ -algebra of a generalized Boolean dynamical system. As an application, we show that gauge-invariant ideals of C ∗ -algebras of generalized Boolean dynamical systems are themselves C ∗ -algebras of generalized Boolean dynamical systems.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-022-01170-x