{
  "abstract": "We consider in this paper complex Lie groups $\\mathrm{SL}_n(\\mathbb{C})$ for $n\\geq 2$, $\\mathrm{SO}_n(\\mathbb{C})$ for $n\\geq 5$, and $\\mathrm{Sp}_{2n}(\\mathbb{C})$ for $n\\geq 1$. We show that for any such Lie group, the Lie algebra of polynomial vector fields can be generated by three $\\mathbb{C}$-complete polynomial vector fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02144",
  "author_total": 2,
  "authors": [
    {
      "name": "Yiyang Jiang"
    },
    {
      "name": "Xudong Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/655jnjr3j1n2e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02144",
  "fulltext_url": null,
  "id": "655jnjr3j1n2e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02144",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7207674081",
  "pdf_url": "https://arxiv.org/pdf/2609.02144",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/655jnjr3j1n2e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02144",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02144"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups",
  "title_text": "Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/655jnjr3j1n2e",
  "venue": "arXiv",
  "versions": []
}