{
  "id": "1608.07645",
  "version": "v1",
  "published": "2016-08-27T01:59:51.000Z",
  "updated": "2016-08-27T01:59:51.000Z",
  "title": "An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra",
  "authors": [
    "Shigeyuki Morita",
    "Takuya Sakasai",
    "Masaaki Suzuki"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AT",
    "math.GT",
    "math.QA"
  ],
  "abstract": "We construct an abelian quotient of the symplectic derivation Lie algebra $\\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental representation of $\\mathrm{Sp}(2g,\\mathbb{Q})$. More specifically, we show that the weight $12$ part of the abelianization of $\\mathfrak{h}_{g,1}$ is $1$-dimensional for $g \\ge 8$. The computation is done with the aid of computers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-27T01:59:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28",
      "20J06",
      "17B40"
    ],
    "keywords": [
      "symplectic derivation lie algebra",
      "free lie algebra",
      "abelian quotient",
      "fundamental representation",
      "abelianization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}