{
  "abstract": "Let $F$ be an algebraically closed field of characteristic $7$, and let $V=L(\\frac12,0)_F$. For the degree-four singular vector $q=(L(-2)^2-2L(-4))\\mathbf1$ in the universal vacuum vertex operator algebra $\\bar V$, set $V_q=\\bar V/I(q)$. We prove that the natural quotient map induces an isomorphism $A_1(V_q)\\cong A_1(V)\\cong F[T]/(T(T-4)(T-5))\\cong F^3$. Explicit $O_1(V_q)$-relations and four families of triangular PBW straightening relations give the upper bound, while three one-dimensional homogeneous subspaces give the matching lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15448",
  "author_total": 1,
  "authors": [
    {
      "name": "Haihua Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mhwtq3p9n0mn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15448",
  "fulltext_url": null,
  "id": "4mhwtq3p9n0mn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15448",
  "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.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221785696",
  "pdf_url": "https://arxiv.org/pdf/2610.15448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mhwtq3p9n0mn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The First Modular Zhu Algebra of $L(\\frac12,0)_F$ in Characteristic Seven",
  "title_text": "The First Modular Zhu Algebra of L(1/2,0)_F in Characteristic Seven",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4mhwtq3p9n0mn",
  "venue": "arXiv",
  "versions": []
}