Some Constructions on Quantum Principal Bundles

[2502.19702] Some Constructions on Quantum Principal Bundles Skip to main content Search Submit Donate Log in Mathematics > Quantum Algebra arXiv:2502.19702 (math) [Submitted on 27 Feb 2025 ( v1 ), last revised 27 Aug 2026 (this version, v6)] Title: Some Constructions on Quantum Principal Bundles Authors: Gustavo Amilcar Saldaña Moncada View PDF HTML (experimental) Abstract: This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove four statements in the theory of quantum principal bundles:: 1) The universal differential envelope $\ast$--calculus of a matrix (compact) Lie group, for the classical bicovariant $\ast$--First Order Differential Calculus, is the algebra of differential forms. 2) An example of a quantum principal bundle in which the space of base forms is not generated by the base space. 3) The group isomorphism between convolution-invertible maps and covariant left module isomorphisms at the level of differential calculus 4) The way the maps $\{T^V_k \}$ from Remark 3.1 look in differential geometry. Subjects: Quantum Algebra (math.QA) MSC classes: 46L87, 58B99 Cite as: arXiv:2502.19702 [math.QA] (or arXiv:2502.19702v6 [math.QA] for this version) https://doi.org/10.48550/arXiv.2502.19702 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gustavo Amilcar Saldaña [ view email ] [v1] Thu, 27 Feb 2025 02:42:58 UTC (16 KB) [v2] Sat, 1 Mar 2025 21:59:44 UTC (16 KB) [v3] Thu, 10 Apr 2025 16:58:33 UTC (16 KB) [v4] Mon, 19 May 2025 23:07:35 UTC (16 KB) [v5] Sun, 1 Feb 2026 19:40:49 UTC (19 KB) [v6] Thu, 27 Aug 2026 23:27:23 UTC (22 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2025-02 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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