Abstract
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.
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The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2020R1A4A3079066).
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de Castro, G.G., Kang, E.J. \(C^*\)-algebras of generalized Boolean dynamical systems as partial crossed products. J Algebr Comb 58, 355–385 (2023). https://doi.org/10.1007/s10801-022-01170-x
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DOI: https://doi.org/10.1007/s10801-022-01170-x
Keywords
- Generalized Boolean dynamical systems
- \(C^*\)-algebras
- Partial actions
- Partial crossed products
- Gauge-invariant ideals
- Graded ideals