On complete generators of certain Lie algebras on Danielewski surfaces

[2406.14702] On complete generators of certain Lie algebras on Danielewski surfaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2406.14702 (math) [Submitted on 20 Jun 2024 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: On complete generators of certain Lie algebras on Danielewski surfaces Authors: Rafael B. Andrist View a PDF of the paper titled On complete generators of certain Lie algebras on Danielewski surfaces, by Rafael B. Andrist View PDF HTML (experimental) Abstract: We study the Lie algebra of polynomial vector fields on a smooth Danielewski surface of the form $x y = p(z)$ with $x,y,z \in \mathbb{C}$. We provide explicitly given generators to show that: 1. The Lie algebra of polynomial vector fields is generated by $6$ complete vector fields. 2. The Lie algebra of volume-preserving polynomial vector fields is generated by finitely many vector fields, whose number depends on the degree of the defining polynomial. 3. There exists a Lie sub-algebra generated by $4$ LNDs whose flows generate a group that acts infinitely transitively on the Danielewski surface. The latter result is also generalized to higher dimensions where $z \in \mathbb{C}^N$. Subjects: Complex Variables (math.CV) ; Algebraic Geometry (math.AG) MSC classes: 32M17, 32E30, 32Q56, 14R10, 14R20 Cite as: arXiv:2406.14702 [math.CV] (or arXiv:2406.14702v3 [math.CV] for this version) https://doi.org/10.48550/arXiv.2406.14702 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Rafael Benedikt Andrist [ view email ] [v1] Thu, 20 Jun 2024 19:50:50 UTC (12 KB) [v2] Thu, 11 Jul 2024 18:17:40 UTC (16 KB) [v3] Thu, 9 Apr 2026 22:51:25 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled On complete generators of certain Lie algebras on Danielewski surfaces, by Rafael B. Andrist View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2024-06 Change to browse by: math math.AG 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

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