{
  "abstract": "We describe all degenerations of complex $4$-dimensional Jordan algebras and of complex $5$-dimensional nilpotent Jordan algebras. The proofs do not use other papers on degenerations, and all degenerations and non-degenerations were formally verified in the proof assistant Lean~4. The graph of primary degenerations of $4$-dimensional Jordan algebras has $73$ vertices and $160$ edges. The variety of $5$-dimensional nilpotent Jordan algebras is stratified into $63$ normal forms, five of which are one- or two-parameter families; together with two special members of a family this gives $65$ objects, and the graph of primary degenerations has $154$ edges. In particular, we describe all irreducible components of the corresponding varieties: the variety of $4$-dimensional Jordan algebras has $10$ irreducible components, and the variety of $5$-dimensional nilpotent Jordan algebras has dimension $22$ and $5$ irreducible components.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31179",
  "author_total": 5,
  "authors": [
    {
      "name": "Victor Bovdi"
    },
    {
      "name": "Ivan Kaygorodov"
    },
    {
      "name": "Yury Popov"
    },
    {
      "name": "Azamat Saydaliyev"
    },
    {
      "name": "Yury Volkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sw6rn6pkznvf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31179",
  "fulltext_url": null,
  "id": "0sw6rn6pkznvf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31179",
  "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": "W7223275676",
  "pdf_url": "https://arxiv.org/pdf/2610.31179",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sw6rn6pkznvf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31179",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31179"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Degenerations of Jordan algebras",
  "title_text": "Degenerations of Jordan algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/0sw6rn6pkznvf",
  "venue": "arXiv",
  "versions": []
}