{
  "abstract": "A pseudo-Euclidean Novikov superalgebra $A$ is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form $\\langle, \\rangle$ such that all left multiplication operators are $\\langle, \\rangle$-antisymmetric. In this case, the associated Lie superalgebra $(A^{-},\\langle, \\rangle)$ is a flat pseudo-Euclidean Lie superalgebra. In this paper, we investigate the structure of pseudo-Euclidean Novikov superalgebras. In particular, we introduce a distinguished subclass, called \\emph{Milnor superalgebras}, and prove that any pseudo-Euclidean Novikov superalgebra whose two-sided ideal is non-degenerate belongs to this class. We provide a method for constructing pseudo-Euclidean Novikov superalgebras. We also introduce a double extension procedure for pseudo-Euclidean Novikov superalgebras and show that every such superalgebra with a degenerate two-sided ideal can be obtained via this method. Furthermore, we establish that any pseudo-Euclidean Novikov superalgebra is either a Milnor superalgebra or can be obtained by a sequence of double extensions starting from a Milnor superalgebra. As an application, we provide a complete classification of pseudo-Euclidean Novikov superalgebras of total dimension at most four over the field of real numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.20775",
  "author_total": 3,
  "authors": [
    {
      "name": "Said Benayadi"
    },
    {
      "name": "Sofiane Bouarroudj"
    },
    {
      "name": "Hamza El Ouali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj9wvacpnaqmb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.20775",
  "fulltext_url": null,
  "id": "bj9wvacpnaqmb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.20775",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7161969029",
  "pdf_url": "https://arxiv.org/pdf/2605.20775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj9wvacpnaqmb.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:19Z",
      "native_id": "2605.20775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.20775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Pseudo-Euclidean Novikov Superalgebras: Structure and Properties",
  "title_text": "Pseudo-Euclidean Novikov Superalgebras: Structure and Properties",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/bj9wvacpnaqmb",
  "venue": "arXiv",
  "versions": []
}