{
  "id": "math/0608673",
  "version": "v2",
  "published": "2006-08-28T06:05:35.000Z",
  "updated": "2009-04-06T17:07:56.000Z",
  "title": "Lie algebras of symplectic derivations and cycles on the moduli spaces",
  "authors": [
    "Shigeyuki Morita"
  ],
  "comment": "This is the version published by Geometry & Topology Monographs on 25 February 2008",
  "journal": "Geom. Topol. Monogr. 13 (2008) 335-354",
  "doi": "10.2140/gtm.2008.13.335",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "We consider the Lie algebra consisting of all derivations on the free associative algebra, generated by the first homology group of a closed oriented surface, which kill the symplectic class. We find the first non-trivial abelianization of this Lie algebra and discuss its relation to unstable cohomology classes of the moduli space of curves via a theorem of Kontsevich.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-06T17:07:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B40",
      "17B56",
      "32G15"
    ],
    "keywords": [
      "moduli space",
      "symplectic derivations",
      "first homology group",
      "first non-trivial abelianization",
      "free associative algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8673M"
    }
  }
}