{
  "abstract": "We establish that, for a binary operad Var, the Hadamard product of Var and the operad Nov of Novikov algebras is a binary operad (i.e., coincides with their Manin white product Nov $\\circ$ Var) if and only if the quadratic part of Var governs a 2-variety. The condition Nov $\\circ$ Var $=$ Nov $\\otimes$ Var is known to be equivalent to the existence of an easily verifiable characterization of those differential Var-polynomials which lie in the free derived Var-algebra. For a binary quadratic operad, these conditions are also equivalent to the Dong property of formal distributions. We distinguish the white product defined as a generated sub-operad from its quadratic approximation and give an example in which the canonical epimorphism between them is not injective.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01798",
  "author_total": 2,
  "authors": [
    {
      "name": "P. Kolesnikov"
    },
    {
      "name": "B. Sartayev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7j9w27f1sqhrr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01798",
  "fulltext_url": null,
  "id": "7j9w27f1sqhrr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01798",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7216003866",
  "pdf_url": "https://arxiv.org/pdf/2610.01798",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7j9w27f1sqhrr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01798",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01798"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Weight Criterion, Dong Property, and Manin Products of Operads",
  "title_text": "The Weight Criterion, Dong Property, and Manin Products of Operads",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/7j9w27f1sqhrr",
  "venue": "arXiv",
  "versions": []
}