$C^{\ast }$-algebras associated to Boolean dynamical systems

The goal of these notes is to present the C*-algebra $C^{\ast }(B,L,\theta )$ of a Boolean dynamical system $(B,L,\theta )$, that generalizes the $C^{\ast }$-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