{
  "abstract": "For restricted simple Cartan-type Lie algebras over an algebraically closed field of characteristic $p\\ge5$, the reduced enveloping algebra at every nonzero $p$-character is a matrix algebra over a terminal symmetric corner, and this corner determines the extensions. Central-socle traces recover its radical and its simple factors, and the first radical layer determines the degree-one extensions. For the Witt algebra $W(1;1)$, at even height $2\\le h\\le p-3$, the unique simple module has self-extension dimension $\\min\\{p-h-2,h+2\\}$. At height two in characteristic seven, we present the Yoneda algebra as an eight-dimensional symmetric algebra tensored with a polynomial algebra on three central degree-two classes. An equivariant Tate resolution and cocycle identities prove the presentation in all degrees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02683",
  "author_total": 1,
  "authors": [
    {
      "name": "Chao Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x9h4jfs0pm0x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02683",
  "fulltext_url": null,
  "id": "9x9h4jfs0pm0x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02683",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02683",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x9h4jfs0pm0x.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02683",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02683"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Extensions at Nonzero p-Characters for Cartan-Type Lie Algebras",
  "title_text": "Extensions at Nonzero p-Characters for Cartan-Type Lie Algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9x9h4jfs0pm0x",
  "venue": "arXiv",
  "versions": []
}