Groupoids associated to self-similar groupoids

Abstract

Let E be a row-finite directed graph without sources. Let G be a discrete groupoid. The groupoid
G acts self-similarly on E with the unit space G(0) = E0. We write this self-similar action of G on E as the pair
(G,E). To our more general situation, we follow Brownlowe et al (2023) to construct two groupoids associated
with (G,E), namely the groupoid S(G,E) ⋉ E∞ and G(G,E). We explore the interplay between the groupoid
S(G,E) ⋉ E∞ and G(G,E), and the structure of G(G,E) is derived.