{
  "id": "0710.5588",
  "version": "v3",
  "published": "2007-10-30T09:08:54.000Z",
  "updated": "2010-01-25T10:23:55.000Z",
  "title": "Hall algebras associated to triangulated categories, II: almost associativity",
  "authors": [
    "Fan Xu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "By using the approach in \\cite{XX2006} to Hall algebras arising in homologically finite triangulated categories, we find an `almost' associative multiplication structure for indecomposable objects in a 2-periodic triangulated category. As an application, we give a new proof of the theorem of Peng and Xiao in \\cite{PX2000} which provides a way of realizing symmetrizable Kac-Moody algebras and elliptic Lie algebras via 2-periodic triangulated categories.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-25T10:23:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B67"
    ],
    "keywords": [
      "triangulated category",
      "hall algebras",
      "associativity",
      "elliptic lie algebras",
      "homologically finite triangulated categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5588X"
    }
  }
}