C⁎-algebras associated to Boolean dynamical systems

The goal of these notes is to present the C⁎-algebra C⁎(B,L,θ) of a Boolean dynamical system (B,L,θ), 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.