Higman-Thompson groups from self-similar groupoid actions

2021/08/02 by Valentin Deaconu, Deaconu, Valentin · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2108.01178

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a self-similar 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 Higman-Thompson 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 AH-conjecture for \mathcal G(G,E) in some particular cases.

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