{
  "abstract": "In this paper, we introduce generalized mock-Poisson algebras as a mock analogue of generalized Poisson algebras. We prove that $A_\\ast^3$ is an ideal annihilated by both operations and that the quotient $A/A_\\ast^3$ is a mock-Poisson algebra. We also show that the dimension seven is the smallest dimension in which a generalized mock-Poisson algebra need not be a mock-Poisson algebra. We give several constructions using derivations, anti-Zinbiel algebras, tensor products, and one-dimensional extensions. We study polarization and depolarization and characterize the corresponding admissible algebras. We prove that every finite-dimensional generalized mock-Poisson algebra over a field of characteristic zero is nilpotent. Finally, we describe representations in terms of semidirect products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23143",
  "author_total": 1,
  "authors": [
    {
      "name": "Zafar Normatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ctaz1hbx0k0xd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23143",
  "fulltext_url": null,
  "id": "ctaz1hbx0k0xd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23143",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7222987062",
  "pdf_url": "https://arxiv.org/pdf/2610.23143",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ctaz1hbx0k0xd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23143",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23143"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Generalized Mock-Poisson Algebras: Constructions and Structural Properties",
  "title_text": "Generalized Mock-Poisson Algebras: Constructions and Structural Properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/ctaz1hbx0k0xd",
  "venue": "arXiv",
  "versions": []
}