{
  "abstract": "We introduce $δ$-mock-Novikov algebras as a parameter-dependent mock analogue of Novikov algebras. For $δ=1$, the commutator of a mock-Novikov algebra defines a Malcev algebra. Every $δ$-mock-Novikov algebra satisfying $\\mathcal{A}^2\\subseteq\\operatorname{Ann}(\\mathcal{A})$ is shown to be differentially special. At the operadic level, the binary quadratic operad governing $δ$-mock-Novikov algebras is quadratically self-dual but not Koszul. We prove that finite-dimensional $δ$-mock-Novikov algebras are nilpotent in characteristic zero and classify those of dimension at most four. Finally, we study the associated Poisson-type structures and establish relations and constructions among them via polarization, depolarization, and tensor products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06913",
  "author_total": 2,
  "authors": [
    {
      "name": "Jie Ruan"
    },
    {
      "name": "Zafar Normatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqarfhqn43rey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06913",
  "fulltext_url": null,
  "id": "aqarfhqn43rey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06913",
  "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": "W7212027658",
  "pdf_url": "https://arxiv.org/pdf/2609.06913",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqarfhqn43rey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06913",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06913"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$δ$-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions",
  "title_text": "δ-Mock-Novikov Algebras: Structural Theory, Operad and Poisson-Type Constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/aqarfhqn43rey",
  "venue": "arXiv",
  "versions": []
}