{
  "abstract": "We extend the theory of commutative exact algebras in braided finite tensor categories (Shimizu-Yadav) to superalgebras, motivated by extensions of vertex operator (super)algebras. For a braided category $\\C$ let $\\B=\\C^{\\gr}$ be the category of $\\mathbb Z/2$-graded objects with the Koszul-signed braiding. It is the underlying category of the supercategory of Creutzig-Kanade-McRae. A supercommutative superalgebra $A=A_0\\oplus A_1$ in $\\C$ is the same as a commutative algebra $\\bA$ in $\\B$, and super-local modules are the local $\\bA$-modules. Hence rigidity, pivotality and ribbon statements are instances of the ordinary theorems, with the ribbon condition $θ_{A_0}=\\id$, $θ_{A_1}=\\varepsilon\\,\\id$, where $\\varepsilon=\\pm1$ is fixed by the statistics of the odd part. For $\\C$ non-degenerate and $\\bA$ haploid and exact we prove that the category of super-local modules is a braided finite tensor category whose Müger center is $\\mathsf{sVect}$. It is the centralizer of a fermion in a non-degenerate category obtained by condensing in $\\C\\boxtimes(\\text{toric code})$. If $\\C$ is ribbon and $\\bA$ is symmetric Frobenius it is ribbon. We construct examples from graded simple currents, treat the free fermion and the symplectic fermion, and compare with Creutzig-Kanade-McRae and Creutzig-McRae-Shimizu-Yadav.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24568",
  "author_total": 1,
  "authors": [
    {
      "name": "A. Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v8v1qme03f3f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24568",
  "fulltext_url": null,
  "id": "6v8v1qme03f3f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24568",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223035595",
  "pdf_url": "https://arxiv.org/pdf/2610.24568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v8v1qme03f3f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.24568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Commutative exact superalgebras and super-modular tensor categories",
  "title_text": "Commutative exact superalgebras and super-modular tensor categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/6v8v1qme03f3f",
  "venue": "arXiv",
  "versions": []
}