{
  "abstract": "We give the geometric classification of complex 3-dimensional Novikov-Poisson and Gelfand-Dorfman algebras. In particular, we prove that the variety of complex 3-dimensional Novikov-Poisson algebras is 12-dimensional; it has 4 irreducible components and has no rigid algebras; the variety of complex 3-dimensional Gelfand-Dorfman algebras is 11-dimensional; it has 10 irreducible components and has 3 rigid algebras. As an additional result, we have the geometric classification of complex 3-dimensional Novikov algebras: it is 9-dimensional, and it has $4$ irreducible components with one rigid algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14010",
  "author_total": 4,
  "authors": [
    {
      "name": "Zeyu Hao"
    },
    {
      "name": "Ivan Kaygorodov"
    },
    {
      "name": "Azamat Saydaliyev"
    },
    {
      "name": "Ziyi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07q9p77395yes.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14010",
  "fulltext_url": null,
  "id": "07q9p77395yes",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14010",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221797492",
  "pdf_url": "https://arxiv.org/pdf/2610.14010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07q9p77395yes.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras",
  "title_text": "The geometric classification of Novikov-Poisson and Gelfand-Dorfman algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/07q9p77395yes",
  "venue": "arXiv",
  "versions": []
}