$C^*$-algebras associated to Boolean dynamical systems

TL;DR

This paper introduces a new class of C*-algebras derived from Boolean dynamical systems, generalizing previous models, and analyzes their structural properties including simplicity, ideals, and K-Theory.

Contribution

It extends the framework of C*-algebras to Boolean dynamical systems, providing new insights into their algebraic and topological properties.

Findings

Characterization of simplicity conditions

Description of gauge invariant ideals

Computation of K-Theory for these algebras

Abstract

The goal of these notes is to present the C*-algebra $C^*(B,L,\theta)$ of a Boolean dynamical system $(B,L,\theta)$, that generalizes the $C^*$-algebra associated to Labelled graphs introduced by Bates and Pask, and to determine its simplicity, its gauge invariant ideals, as well as compute its K-Theory