The goal of this talk is to present the C*-algebra $C^*(\mathcal{B}, \mathcal{L}, \theta)$ of a Boolean dynamical system $(\mathcal{B}, \mathcal{L}, \theta)$, that generalizes the $C^*$-algebra associated to a labelled graph introduced by Bates and Pask, and to determine its simplicity, its gauge invariant ideals, as well as compute its K-Theory.
This is a joint work with Toke Meier Carlsen (Department of Science and Technology, University of the Faroe Islands) and Eduard Ortega (Department of Mathematical Sciences, NTNU Trondheim).
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