{"paper":{"title":"Higman-Thompson groups from self-similar groupoid actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Valentin Deaconu","submitted_at":"2021-08-02T21:24:14Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01178","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.01178/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}