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)} &#8905-E^&#8734- and G_{(G,E)}. We explore the interplay between the groupoid S_{(G,E)}&#8905-E^&#8734- and G_{(G,E)} and how powerful they are.

Keywords: Groupoids, Graphs, Self-Similar Action

Topic: Mathematics and Mathematics Education