{
  "abstract": "We study regular $\\mathbb{N}$-graded vertex operator algebras $V=\\bigoplus_{n\\geq 0}V_n$ whose weight-zero algebra $V_0$ is a nontrivial finite-dimensional local Gorenstein algebra, asking which structural features of strongly rational vertex operator algebras persist without the CFT-type condition $V_0=\\mathbb{C}{\\bf 1}$. For semisimple Lie subalgebras of the left Leibniz algebra $V_1$, assuming $\\ker\\left(\\left.L(-1)\\right|_{V_0}\\right)=\\mathbb{C}\\mathbf{1}$, the product $u_1v$ induces an invariant symmetric bilinear form. Under $C_2$-cofiniteness and a nondegeneracy condition, each simple component with nonzero form generates an affine vertex operator algebra at positive integral level and acts integrably on $V$. When $V_1$ is solvable, the Frobenius structure of $V_0$ yields a distinguished nondegenerate subspace $M\\subset V_1$. Under a quasi-primary condition, $M$ is abelian and generates a Heisenberg vertex operator algebra. With additional semisimplicity, full-rank integrality, and cocycle compatibility assumptions, $V$ contains a conformally embedded lattice vertex operator algebra $V_K$, where $K$ is positive-definite and even, with rank $\\dim_{\\mathbb{C}}M$ and minimum norm at least $4$. Conformally shifted lattice vertex operator algebras provide explicit models illustrating the distinction among weight-one Lie, mode-generated Lie, and lattice structures. They also show that regularity alone does not ensure semisimplicity of arbitrary Heisenberg zero-mode actions, so the additional lattice-theorem hypotheses represent genuine structural obstructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22780",
  "author_total": 1,
  "authors": [
    {
      "name": "Gaywalee Yamskulna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brf2pt286vmy9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22780",
  "fulltext_url": null,
  "id": "brf2pt286vmy9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22780",
  "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": "W7214046507",
  "pdf_url": "https://arxiv.org/pdf/2609.22780",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brf2pt286vmy9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22780",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22780"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Affine and Lattice Structures in Regular $\\mathbb{N}$-Graded Vertex Operator Algebras with Gorenstein $V_0$",
  "title_text": "Affine and Lattice Structures in Regular ℕ-Graded Vertex Operator Algebras with Gorenstein V_0",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/brf2pt286vmy9",
  "venue": "arXiv",
  "versions": []
}