$$C^*$$-algebras of generalized Boolean dynamical systems as partial crossed products

• DOI: 10.1007/s10801-022-01170-x
• Publication Date: 2022-09-26T20:37:22Z
• Authors: Gilles G. de Castro; Eun Ji Kang
• Keywords: Crossed product; Complete Boolean algebra; Free Boolean algebra; Interior algebra

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 system.<br/>28 pages. arXiv admin note: text overlap with arXiv:2106.09366<br/>