{
  "id": "math/0505614",
  "version": "v1",
  "published": "2005-05-27T15:31:27.000Z",
  "updated": "2005-05-27T15:31:27.000Z",
  "title": "Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups",
  "authors": [
    "Nantel Bergeron",
    "Yun Gao",
    "Naihong Hu"
  ],
  "comment": "25 pages AMSTeX",
  "journal": "J. Algebra 301 (2006), no. 1, 378-405",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We find the defining structures of two-parameter quantum groups $U_{r,s}(\\frak g)$ corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between $(U_{r,s}(\\frak g), < ,>)$ and its associated object $(U_{s^{-1}, r^{-1}}(\\frak g), < | >)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-27T15:31:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "81R50"
    ],
    "keywords": [
      "two-parameter quantum groups",
      "lusztigs symmetries",
      "drinfeld doubles",
      "symplectic lie algebras",
      "environment conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5614B"
    }
  }
}