Limit dynamical systems and C∗-algebras from self-similar graph actions

Abstract

In this article, we study dynamical and $C^{\ast }$-algebraic properties of self-similar group actions on finite directed graphs. We investigate the structure of limit dynamical systems induced from group actions on graphs, and we deduce conditions of group actions and graphs for the groupoid $C^{\ast }$-algebras defined by limit dynamical systems to be simple, separable, purely infinite, nuclear, and satisfying the universal coefficient theorem.