{
  "abstract": "A biderivation of an algebra is a bilinear map which is a derivation in each argument. We describe all biderivations of finite-dimensional complex null-filiform and filiform Zinbiel algebras. For the n-dimensional null-filiform algebra, every biderivation is determined by an arbitrary value at its generating pair; the space of biderivations has dimension n and consists entirely of symmetric maps. For the three standard filiform families, we give explicit bases and determine their symmetric and skew-symmetric parts. We also treat all filiform algebras of dimensions at most four, including the exceptional families not covered by the classification in dimensions at least five. A three-dimensional algebra admits a three-dimensional space of skew-symmetric biderivations, two of which have values outside its annihilator. Up to isomorphism, it is the unique complex filiform Zinbiel algebra with this property. The proofs use generators, annihilator-valued maps, a truncated polynomial model, and conformal endomorphisms of bilinear forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32550",
  "author_total": 1,
  "authors": [
    {
      "name": "Arislanbay Abdireymov. Bakhtiyor Yusupov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfq8ysfb9y3xj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32550",
  "fulltext_url": null,
  "id": "cfq8ysfb9y3xj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32550",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7223651141",
  "pdf_url": "https://arxiv.org/pdf/2610.32550",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfq8ysfb9y3xj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32550",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32550"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Biderivations of Null-Filiform and Filiform Zinbiel Algebras",
  "title_text": "Biderivations of Null-Filiform and Filiform Zinbiel Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/cfq8ysfb9y3xj",
  "venue": "arXiv",
  "versions": []
}