{
  "id": "1009.5457",
  "version": "v6",
  "published": "2010-09-28T06:22:40.000Z",
  "updated": "2011-08-07T09:01:09.000Z",
  "title": "The topology of a semisimple Lie group is essentially unique",
  "authors": [
    "Linus Kramer"
  ],
  "comment": "To appear in: Advances in Mathematics",
  "categories": [
    "math.GR",
    "math.GN"
  ],
  "abstract": "We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\\sigma$-compact group $\\Gamma$ is automatically a homeomorphism, provided that $S$ is absolutely simple. If $S$ is complex, then non-continuous field automorphisms of the complex numbers have to be considered, but that is all.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-08-07T09:01:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie group",
      "essentially unique",
      "study locally compact group topologies",
      "lie group topology",
      "non-continuous field automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.5457K"
    }
  }
}