{
  "abstract": "In this paper, we introduce the notion of an omni-representation of a Leibniz conformal algebra $\\mathfrak{g}$ on a $\\mathbb{C}[\\partial]$-module $M$ as a Leibniz conformal algebra homomorphism from $\\mathfrak{g}$ to the conformal omni-Lie algebra $\\mathfrak{gc}(M)\\oplus M$. We show that the right $λ$-action of a representation induces a Maurer--Cartan element. When $M$ is a free $\\mathbb{C}[\\partial]$-module of finite rank, it also defines, via the conformal dual $M_c^*$, a $1$-cocycle with values in $M_c^*\\otimes M\\cong\\mathfrak{gc}(M)$. Consequently, every such representation gives rise to an omni-representation on $M_c^*\\otimes M$. We characterize omni-representations with values in the graph of a conformal embedding tensor. Finally, we introduce the omni-cohomology theory of Leibniz conformal algebras and establish the relation between omni-cohomology groups and the usual cohomology groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33856",
  "author_total": 1,
  "authors": [
    {
      "name": "Sami Benabdelhafidh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7gx67ta4wrfjn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33856",
  "fulltext_url": null,
  "id": "7gx67ta4wrfjn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33856",
  "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": "W7223859467",
  "pdf_url": "https://arxiv.org/pdf/2610.33856",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7gx67ta4wrfjn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33856",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33856"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Omni-representations of Leibniz conformal algebras",
  "title_text": "Omni-representations of Leibniz conformal algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/7gx67ta4wrfjn",
  "venue": "arXiv",
  "versions": []
}