{
  "abstract": "Let $\\mathfrak{g}$ be a basic classical Lie superalgebra and let $\\widehat{\\mathfrak{g}}$ be the corresponding affine Lie superalgebra. In this paper, we first prove that a Cartan subalgebra acts semisimply on ordinary modules for the simple affine vertex operator superalgebra $L_{\\widehat{\\mathfrak{g}}}(k,0)$ at boundary admissible level $k$. Then we prove that the category $\\mathcal{O}_{k}^{ord}(\\mathfrak{g})$ of ordinary $L_{\\widehat{\\mathfrak{g}}}(k,0)$-modules is finite, semisimple and $\\mathcal{O}_{k}^{ord}(\\mathfrak{g})$ is exactly the category $KL_k(\\mathfrak{g})$ of finite-length generalized modules for the affine vertex operator superalgebra $L_{\\widehat{\\mathfrak{g}}}(k,0)$.Thus $\\mathcal{O}_{k}^{ord}(\\mathfrak{g})$ is a braided tensor supercategory. Furthermore, we obtain the rigidity of the supercategory $\\mathcal{O}_{k}^{ord}(\\mathfrak{g})$ and thus it is a ribbon supercategory. Finally, we conclude that $\\mathcal{O}_{k}^{ord}(\\mathfrak{g})$ is a ribbon fusion supercategory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01774",
  "author_total": 2,
  "authors": [
    {
      "name": "Huaimin Li"
    },
    {
      "name": "Qing Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fp234v0wq19n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01774",
  "fulltext_url": null,
  "id": "3fp234v0wq19n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01774",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7215810850",
  "pdf_url": "https://arxiv.org/pdf/2610.01774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fp234v0wq19n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ordinary modules for affine vertex operator superalgebras",
  "title_text": "Ordinary modules for affine vertex operator superalgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/3fp234v0wq19n",
  "venue": "arXiv",
  "versions": []
}