{
  "id": "quant-ph/0209113",
  "version": "v2",
  "published": "2002-09-20T18:22:22.000Z",
  "updated": "2002-12-04T20:23:38.000Z",
  "title": "Diameters of Homogeneous Spaces",
  "authors": [
    "Michael Freedman",
    "Alexei Kitaev",
    "Jacob Lurie"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |_{G} which induces a bi-invariant metric d_G(x,y)=|Ad(yx^{-1})|_{G} on G. We prove the existence of a constant \\beta \\approx .12 (independent of G) such that for any closed subgroup H \\subsetneq G, the diameter of the quotient G/H (in the induced metric) is \\geq \\beta.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-04T20:23:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homogeneous spaces",
      "compact connected lie group",
      "trivial center",
      "lie algebra",
      "operator norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002quant.ph..9113F"
    }
  }
}