[2608.14482] AF-action groupoid models for diagonal AH-algebras Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Operator Algebras arXiv:2608.14482 (math) [Submitted on 14 Aug 2026] Title: AF-action groupoid models for diagonal AH-algebras Authors: Ali Imad Raad , Jonathan Taylor View a PDF of the paper titled AF-action groupoid models for diagonal AH-algebras, by Ali Imad Raad and 1 other authors View PDF HTML (experimental) Abstract: We show that an inductive AH-system with diagonal connecting maps describes an action of the canonical AF-groupoid on the spectrum of the canonical C$^*$-diagonal, and that the canonical groupoid model is given by the transformation groupoid associated to this action. This divides the groupoid structure into two distinct aspects: the acting AF-groupoid (which is well-studied) and the unit space on which it acts. We describe the unit space by enriching the Bratteli diagram with extra topological information, and apply these descriptions to examples of interest, including Villadsen algebras of the first kind. Comments: 18 pages Subjects: Operator Algebras (math.OA) ; Functional Analysis (math.FA) MSC classes: Primary 46L05, Secondary 22A22 Cite as: arXiv:2608.14482 [math.OA] (or arXiv:2608.14482v1 [math.OA] for this version) https://doi.org/10.48550/arXiv.2608.14482 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ali Imad Raad [ view email ] [v1] Fri, 14 Aug 2026 16:59:08 UTC (24 KB) Full-text links: Access Paper: View a PDF of the paper titled AF-action groupoid models for diagonal AH-algebras, by Ali Imad Raad and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OA < prev | next > new | recent | 2026-08 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from