{
  "abstract": "We study a family of liftings $\\mathfrak U(λ)$ of the super Jordan plane over the infinite cyclic group in characteristic zero. For a nonzero lifting parameter $λ$, we identify a natural subalgebra $\\mathfrak B$ with the bosonization of $U(\\mathfrak{osp}(1|2))$, also known as $sl_{-1}(2)$, and show that the lifting $\\mathfrak U(λ)$ is obtained from $\\mathfrak B$ by an Ore localization at a single distinguished element. This structural description provides a unified approach to the representation theory and ideal structure of $\\mathfrak U(λ)$. We classify the finite-dimensional simple modules of $\\mathfrak B$ and prove that every finite-dimensional $\\mathfrak B$-module is completely reducible; the localization then yields the corresponding results for $\\mathfrak U(λ)$. We determine the prime, primitive, and completely prime ideals of both algebras. Finally, we compute their classical quotient rings, showing in particular that the classical quotient ring of $\\mathfrak U(λ)$ is a $2\\times2$ matrix algebra over the skew field of fractions of the tensor product of its centre and the first Weyl algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10098",
  "author_total": 1,
  "authors": [
    {
      "name": "Tao Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wxv1p6dg7n8b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10098",
  "fulltext_url": null,
  "id": "4wxv1p6dg7n8b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10098",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7220931365",
  "pdf_url": "https://arxiv.org/pdf/2610.10098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wxv1p6dg7n8b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "From bosonized $\\mathfrak{osp}(1|2)$ to liftings of the super Jordan plane",
  "title_text": "From bosonized osp(1|2) to liftings of the super Jordan plane",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/4wxv1p6dg7n8b",
  "venue": "arXiv",
  "versions": []
}