{
  "abstract": "An anti-quadratic nearly associative algebra $(A, \\bullet, ω)$ is a nearly associative algebra equipped with a non-degenerate skew-symmetric bilinear form $ω$ satisfying the anti-associativity condition $ω(u \\bullet v, w) = -ω(u, v \\bullet w)$ for all $u, v, w \\in A.$ In this paper, we investigate the structural properties and extension theory of these algebras. We prove that any anti-quadratic nearly associative algebra is inherently nilpotent of index at most $6$. Furthermore, we introduce a novel $T T^*$-extension method and show that every anti-quadratic nearly associative algebra arises from this construction. We also introduce the notion of a double extension and prove that every such algebra can be constructed by iterated double extensions. Finally, as an application, we give a complete classification of anti-quadratic nearly associative algebras of dimension at most $4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41465",
  "author_total": 2,
  "authors": [
    {
      "name": "Sofiane Bouarroudj"
    },
    {
      "name": "Hamza El Ouali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8qta912ywyj8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41465",
  "fulltext_url": null,
  "id": "8qta912ywyj8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41465",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8qta912ywyj8z.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Anti-quadratic nearly associative algebras",
  "title_text": "Anti-quadratic nearly associative algebras",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/8qta912ywyj8z",
  "venue": "arXiv",
  "versions": []
}