{
  "id": "1103.1241",
  "version": "v2",
  "published": "2011-03-07T11:13:56.000Z",
  "updated": "2011-03-15T18:30:58.000Z",
  "title": "The Ringel--Hall Lie algebra of a spherical object",
  "authors": [
    "Changjian Fu",
    "Dong Yang"
  ],
  "comment": "26pages",
  "doi": "10.1112/jlms/jdr064",
  "categories": [
    "math.RT",
    "math.CT",
    "math.QA"
  ],
  "abstract": "For an integer $w$, let $\\cs_w$ be the algebraic triangulated category generated by a $w$-spherical object. We determine the Picard group of $\\cs_w$ and show that each orbit category of $\\cs_w$ is triangulated and is triangle equivalent to a certain orbit category of the bounded derived category of a standard tube. When $n=2$, the orbit category $\\cs_w/\\Sigma^2$ is 2-periodic triangulated, and we characterize the associated Ringel--Hall Lie algebra in the sense of Peng and Xiao.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-15T18:30:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16E35",
      "16E45",
      "17B99"
    ],
    "keywords": [
      "spherical object",
      "orbit category",
      "associated ringel-hall lie algebra",
      "triangle equivalent",
      "picard group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1241F"
    }
  }
}