HigmanThompson groups from selfsimilar groupoid actions
Abstract
Given a selfsimilar groupoid action $(G,E)$ on a finite directed graph, we prove some properties of the corresponding ample groupoid of germs $\mathcal G(G,E)$. We study the analogue of the HigmanThompson group associated to $(G,E)$ using $G$tables and relate it to the topological full group of $\mathcal G(G,E)$, which is isomorphic to a subgroup of unitaries in the algebra $C^*(G,E)$. After recalling some concepts in groupoid homology, we discuss the Matui's AHconjecture for $\mathcal G(G,E)$ in some particular cases.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.01178
 arXiv:
 arXiv:2108.01178
 Bibcode:
 2021arXiv210801178D
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Dynamical Systems