{
  "id": "math/0406299",
  "version": "v1",
  "published": "2004-06-15T15:49:30.000Z",
  "updated": "2004-06-15T15:49:30.000Z",
  "title": "Conformal holonomy of bi-invariant metrics",
  "authors": [
    "Felipe Leitner"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group $\\SO(4)$. Its conformal holonomy group is calculated to be $\\SO(7)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-15T15:49:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A30",
      "53C29"
    ],
    "keywords": [
      "bi-invariant metric",
      "compact semisimple lie groups",
      "normal conformal cartan connection",
      "conformal holonomy group",
      "conformal geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6299L"
    }
  }
}