{
  "abstract": "We discuss rather basic problems on super principal bundles for $C^{\\infty}$-supermanifolds (over $\\mathbb{R}$) and analytic supermanifolds over a complete field of arbitrary characteristic. Sharper answers are obtained for $C^{\\infty}$-supermanifolds and for homogeneous supermanifolds. Among others, it is proved for $C^{\\infty}$-supermanifolds that given a $C^{\\infty}$-supermanifold $B$ and a super Lie group $G$, there is a natural one-to-one correspondence (up to isomorphism) between the $G$-super principal bundles over $B$ and the $G_{\\mathrm{rd}}$-principal bundles over $B_{\\mathrm{rd}}$, where $G_{\\mathrm{rd}}$ (resp., $B_{\\mathrm{rd}}$) denotes the ordinary Lie group (resp., manifold) associated with $G$ (resp., $B$). To prove this, we show a generalized, equivariant version of the renowned Batchelor Theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25811",
  "author_total": 1,
  "authors": [
    {
      "name": "Akira Masuoka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxm50tg90sjgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25811",
  "fulltext_url": null,
  "id": "fxm50tg90sjgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25811",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7223046135",
  "pdf_url": "https://arxiv.org/pdf/2610.25811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxm50tg90sjgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25811"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Principal bundles in supersymmetry",
  "title_text": "Principal bundles in supersymmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/fxm50tg90sjgt",
  "venue": "arXiv",
  "versions": []
}