Self-similar group actions on ultragraphs and associated $C^{\ast }$-algebras

Abstract

As a generalization of the Exel-Pardo's notion of self-similar graph, we introduce self-similar group actions on ultragraphs and their $C^{\ast }$-algebras. We then approach to the $C^{\ast }$-algebras by inverse semigroup and tight groupoid models.

29 pages