{
  "id": "1211.6881",
  "version": "v1",
  "published": "2012-11-29T11:20:01.000Z",
  "updated": "2012-11-29T11:20:01.000Z",
  "title": "BGP-Reflection Functors and Lusztig's Symmetries of Modified Quantized Enveloping Algebras",
  "authors": [
    "Jie Xiao",
    "Minghui Zhao"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $\\mathbf{U}$ be the quantized enveloping algebra and $\\dot{\\mathbf{U}}$ its modified form. Lusztig gives some symmetries on $\\mathbf{U}$ and $\\dot{\\mathbf{U}}$. Since the realization of $\\mathbf{U}$ by the reduced Drinfeld double of the Ringel-Hall algebra, one can apply the BGP-reflection functors to the double Ringel-Hall algebra to obtain Lusztig's symmetries on $\\mathbf{U}$ and their important properties, for instance, the braid relations. In this paper, we define a modified form $\\dot{\\mathcal{H}}$ of the Ringel-Hall algebra and realize the Lusztig's symmetries on $\\dot{\\mathbf{U}}$ by applying the BGP-reflection functors to $\\dot{\\mathcal{H}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-29T11:20:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B37"
    ],
    "keywords": [
      "modified quantized enveloping algebras",
      "bgp-reflection functors",
      "lusztigs symmetries",
      "modified form",
      "important properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.6881X"
    }
  }
}