{
  "id": "math/0202041",
  "version": "v1",
  "published": "2002-02-05T18:00:11.000Z",
  "updated": "2002-02-05T18:00:11.000Z",
  "title": "Representations of n-Lie algebras",
  "authors": [
    "A. S. Dzhumadil'daev"
  ],
  "comment": "16 pages, LaTeX",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "Let $V_n=<e_1,...,e_{n+1}>$ be a vector products n-Lie algebra with n-Lie commutator $[e_1,...,\\hat{e_i},...,e_{n+1}]=(-1)^ie_i$ over the field of complex numbers. Any finite-dimensional n-Lie $V_n$-module is completely reducible. Any finite-dimensional irreducible n-Lie $V_n$-module is isomorphic to a n-Lie extension of $so_{n+1}$-module with highest weight $t\\pi_1$ for some nonnegative integer t.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-05T18:00:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "22E70"
    ],
    "keywords": [
      "representations",
      "vector products n-lie algebra",
      "complex numbers",
      "highest weight",
      "n-lie commutator"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2041D"
    }
  }
}