Groupoids associated with self-similar groupoids Isnie Yusnitha
Mathematics Study Program, FPMIPA, Universitas Pendidikan Indonesia
Abstract
Let E be a row-finite directed graph without sources. Let G be an amenable discrete groupoid. The groupoid G acts self-similarly on E with the unit space G^{((0))} =E^{0}. 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 how powerful they are.
