{
  "abstract": "We initiate a systematic operadic approach to anti-pre-Lie algebras. We study the operad controlling anti-pre-Lie algebras, its relationship to the operad of Novikov algebras and its cyclic structure. We establish that the Lie bracket of an anti-pre-Lie algebra satisfies the standard identity of degree five. We also establish a quadratic maximality property of the anti-pre-Lie operad with respect to this identity. We then show that the anti-pre-Lie operad and its Koszul dual are not Koszul and give a full description of the latter. Finally, we identify the Lie elements in the Koszul dual operad with the operad of metabelian Lie algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15858",
  "author_total": 4,
  "authors": [
    {
      "name": "Chengming Bai"
    },
    {
      "name": "Vladimir Dotsenko"
    },
    {
      "name": "Guilai Liu"
    },
    {
      "name": "Hongjie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xhwcx9cq3x61.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15858",
  "fulltext_url": null,
  "id": "1xhwcx9cq3x61",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15858",
  "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": "W7221783481",
  "pdf_url": "https://arxiv.org/pdf/2610.15858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xhwcx9cq3x61.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The operad of anti-pre-Lie algebras and its Lie elements",
  "title_text": "The operad of anti-pre-Lie algebras and its Lie elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1xhwcx9cq3x61",
  "venue": "arXiv",
  "versions": []
}