{
  "id": "hep-th/9312004",
  "version": "v1",
  "published": "1993-12-01T16:52:36.000Z",
  "updated": "1993-12-01T16:52:36.000Z",
  "title": "Symplectic structure of the moduli space of flat connections on a Riemann surface",
  "authors": [
    "A. Yu. Alekseev",
    "A. Z. Malkin"
  ],
  "comment": "20 pages",
  "journal": "Commun.Math.Phys.169:99-120,1995",
  "doi": "10.1007/BF02101598",
  "categories": [
    "hep-th",
    "math.DG"
  ],
  "abstract": "We consider canonical symplectic structure on the moduli space of flat ${\\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum of $n$ copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie group $G^{*}$ and $g$ copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group $G$ (the pair ($G,G^{*}$) corresponds to the Lie algebra ${\\g}$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-12-01T16:52:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann surface",
      "moduli space",
      "flat connections",
      "poisson-lie group",
      "semisimple lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 360704
    }
  }
}