{
  "id": "2012.10954",
  "version": "v1",
  "published": "2020-12-20T15:42:13.000Z",
  "updated": "2020-12-20T15:42:13.000Z",
  "title": "Nonlinear realisations of Lie superalgebras",
  "authors": [
    "Jakob Palmkvist"
  ],
  "comment": "25 pages",
  "categories": [
    "math.RT",
    "hep-th",
    "math.RA"
  ],
  "abstract": "For any decomposition of a Lie superalgebra $\\mathcal G$ into a direct sum $\\mathcal G=\\mathcal H\\oplus\\mathcal E$ of a subalgebra $\\mathcal H$ and a subspace $\\mathcal E$, we construct a nonlinear realisation of $\\mathcal G$ on $\\mathcal E$. The result generalises a theorem by Kantor from Lie algebras to Lie superalgebras. When G is a differential graded Lie algebra, it gives a construction of an associated $L_\\infty$-algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-20T15:42:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie superalgebra",
      "nonlinear realisation",
      "differential graded lie algebra",
      "direct sum",
      "result generalises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}