{
  "abstract": "A Lie algebra is said to be $1.5$-generated if every nonzero element can be completed to a two-element generating set. We prove that the Lie algebra of polynomial vector fields with constant divergence on the affine space is $1.5$-generated. We also show that the Lie algebra of all polynomial vector fields on the complex affine space is generated by two completely integrable elements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13798",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Beldiev"
    },
    {
      "name": "Gleb Pogudin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bb437pt2jaytp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13798",
  "fulltext_url": null,
  "id": "bb437pt2jaytp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13798",
  "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"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7203606152",
  "pdf_url": "https://arxiv.org/pdf/2608.13798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bb437pt2jaytp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.13798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Lie algebra of polynomial vector fields on the affine space with constant divergence is $1.5$-generated",
  "title_text": "The Lie algebra of polynomial vector fields on the affine space with constant divergence is $1.5$-generated",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/bb437pt2jaytp",
  "venue": "arXiv",
  "versions": []
}