Zahra Afsar: C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states

Abstract: In a joint work with N. Brownlowe, J. Ramagge and M.F. Whittaker, we introduce the notion of a self-similar action of a groupoid G on a finite higher-rank graph. To such an action, we associate two C*-algebras: the Toeplitz algebra and the Cuntz–Pimsner algebra. We study the KMS states of these algebras in natural dynamics. We then illustrate our results by introducing the notion of a coloured-graph automaton, which we use to construct examples of self-similar actions. We compute the unique KMS states of the Cuntz–Pimsner algebra for some concrete examples.