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Higman-Thompson groups from self-similar groupoid actions

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arxiv 2108.01178 v1 pith:6TMSQHVB submitted 2021-08-02 math.OA math.DS

Valentin Deaconu This is my paper · ORCID
classification math.OAmath.DS
keywords groupoidmathcalsomegrouphigman-thompsonself-similaractionactions
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A graph-theoretical characterisation of subgroups of Thompson's group $V$

    math.GR 2026-08 accept novelty 8.0 of 10

    A finitely generated group embeds in Thompson's group V if and only if it is the transition group of a context-free graph, which rules out intermediate-growth groups and the Basilica and Hanoi Towers groups.

  2. Eventually Self-Similar Groups acting on Fractals

    math.GR 2024-12 conditional novelty 7.0 of 10

    Eventually self-similar groups acting on fractals built from almost expanding hyperedge replacement systems inherit finiteness properties from their self-similar building blocks, yielding F∞ for airplane and dendrite ...

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