{
  "abstract": "Let X be an affine variety. In the present paper, we introduce the notion of a locally integrable Borel subalgebra of the Lie algebra Lie(Aut(X)). We show that these are precisely the tangent algebras of the Borel subgroups of Aut(X). We classify the locally integrable Borel subalgebras in the Lie algebras of the groups Aut(S) of toric affine surfaces S, notably of the affine plane and its cyclic quotients. See [5] for a description of the Borel subgroups and, more generally, maximal solvable subgroups of Aut(S).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "M Zaidenberg"
    },
    {
      "name": "Ivan Arzhantsev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jbtzv2yw6pr1.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8jbtzv2yw6pr1",
  "issns": [],
  "landing_url": "https://hal.science/hal-05843291v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05843291/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jbtzv2yw6pr1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05843291",
      "source": "hal",
      "url": "https://hal.science/hal-05843291v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Borel subalgebras of Lie algebras of vector fields",
  "title_text": "Borel subalgebras of Lie algebras of vector fields",
  "type": "preprint",
  "updated_at": "2026-10-31T12:20:56Z",
  "url": "https://research.draconitic.com/paper/8jbtzv2yw6pr1",
  "venue": "HAL",
  "versions": []
}