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

TL;DR

This paper establishes a correspondence between C*-algebras of generalized Boolean dynamical systems and partial crossed products, providing conditions for isomorphism and analyzing gauge-invariant ideals.

Contribution

It introduces a realization of these C*-algebras as partial crossed products and characterizes gauge-invariant ideals within this framework.

Findings

C*-algebras of generalized Boolean dynamical systems can be represented as partial crossed products.

Provides sufficient conditions for isomorphism between partial crossed products and these C*-algebras.

Gauge-invariant ideals are themselves C*-algebras of generalized Boolean dynamical systems.

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 system.