{
  "abstract": "In this paper, we develop a unified approach for various operators on Lie conformal algebras. Given a quasi-twilled Lie conformal algebra $(\\Ep,\\Vs,\\Ws)$, we introduce two dual families of operators: \\emph{right deformation maps} $D:\\Vs\\to\\Ws$ and \\emph{left deformation maps} $B:\\Ws\\to\\Vs$. Each family simultaneously subsumes several classical structures: modified $r$-matrices, crossed homomorphisms, derivations, and Lie conformal algebra homomorphisms in the right case, relative Rota-Baxter operators, twisted Rota-Baxter operators, Reynolds operators, and deformation maps of matched pairs in the left case. Using Voronov's derived bracket method, we construct the controlling homotopy algebras: a curved $L_\\infty$-algebra governing right deformation maps and an $L_\\infty$-algebra governing left deformation maps, with Maurer-Cartan elements precisely characterizing each type. We further develop the associated deformation theories via twisted $L_\\infty$-algebras and define cohomology complexes for both types of deformation maps, recovering and extending the cohomologies of all classical and conformal operators already developed in the literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.28825",
  "author_total": 3,
  "authors": [
    {
      "name": "Taoufik Chtioui"
    },
    {
      "name": "Sami Mabrouk"
    },
    {
      "name": "Abdenacer Makhlouf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6488m90d61az1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.28825",
  "fulltext_url": null,
  "id": "6488m90d61az1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.28825",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7166713729",
  "pdf_url": "https://arxiv.org/pdf/2606.28825",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6488m90d61az1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.28825",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.28825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Deformation maps on quasi-twilled Lie conformal algebras",
  "title_text": "Deformation maps on quasi-twilled Lie conformal algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6488m90d61az1",
  "venue": "arXiv",
  "versions": []
}