{
  "abstract": "We study the modular class of $Q$-manifolds, and in particular of negatively graded Lie $\\infty$-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that the notion is homotopy invariant. In the process, the adjoint and coadjoint actions up to homotopy of a Lie $\\infty$-algebroid are spelled out. We also wrote down explicitly some dualities, e.g. between representations up to homotopies of Lie $\\infty$-algebroids and their $Q$-manifold equivalent, which we hope to be of use for future reference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2203.16139",
  "author_total": 2,
  "authors": [
    {
      "name": "Raquel Caseiro"
    },
    {
      "name": "Camille Laurent-Gengoux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zng93nfsf1y5.bib",
  "cited_by": 5,
  "doi": "10.3934/jgm.2022008",
  "fulltext_url": null,
  "id": "0zng93nfsf1y5",
  "issns": [
    "1941-4889",
    "1941-4897"
  ],
  "landing_url": "https://hal.science/hal-03632644v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.mphy"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W4226341691",
  "pdf_url": "https://hal.science/hal-03632644/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": "American Institute of Mathematical Sciences (AIMS)",
  "ris": "https://research.draconitic.com/paper/0zng93nfsf1y5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-03632644",
      "source": "hal",
      "url": "https://hal.science/hal-03632644v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:0.phys",
      "subfield": "general"
    }
  ],
  "title": "Modular class of Lie $\\infty$-algebroids and adjoint representations",
  "title_text": "Modular class of Lie ∞-algebroids and adjoint representations",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:27Z",
  "url": "https://research.draconitic.com/paper/0zng93nfsf1y5",
  "venue": "Journal of Geometric Mechanics",
  "versions": []
}