{
  "id": "1304.7335",
  "version": "v1",
  "published": "2013-04-27T07:00:09.000Z",
  "updated": "2013-04-27T07:00:09.000Z",
  "title": "On the cohomology and extensions of first-class $n$-Lie superalgebras",
  "authors": [
    "Yao Ma",
    "Liangyun Chen"
  ],
  "journal": "Commun. Algebra,42(2014)(10),4592-4613",
  "categories": [
    "math.RT"
  ],
  "abstract": "An $n$-Lie superalgebra of parity 0 is called a first-class $n$-Lie superalgebra. In this paper, we give the representation and cohomology for a first-class $n$-Lie superalgebra and obtain a relation between extensions of a first-class $n$-Lie superalgebra $\\mathfrak{b}$ by an abelian one $\\mathfrak{a}$ and $Z^1(\\mathfrak{b}, \\mathfrak{a})_{\\bar{0}}$. We also introduce the notion of $T^*$-extensions of first-class $n$-Lie superalgebras and prove that every finite-dimensional nilpotent metric first-class $n$-Lie superalgebra $(\\g,< ,>_{\\g})$ over an algebraically closed field of characteristic not 2 is isometric to a suitable $T^*$-extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-27T07:00:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie superalgebra",
      "cohomology",
      "finite-dimensional nilpotent metric first-class",
      "representation",
      "algebraically closed field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.7335M"
    }
  }
}