{
  "id": "1208.2639",
  "version": "v2",
  "published": "2012-08-13T16:59:38.000Z",
  "updated": "2012-11-16T00:06:08.000Z",
  "title": "Differentiable vectors and unitary representations of Frechet-Lie supergroups",
  "authors": [
    "Hadi Salmasian",
    "Karl-Hermann Neeb"
  ],
  "comment": "Accepted version (to appear in Mathematische Zeitschrift)",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For a locally convex Lie group with the Trotter property, we prove that the space of k-times differentiable vectors of a unitary representation is equal to the intersection of domains of k-fold products of the Lie algebra action. The result also holds for continuous representations of locally exponential groups on metrizable locally convex spaces. As an application, we extend a key stability theorem in the representation theory of Lie supergroups beyond the Banach case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-16T00:06:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E65",
      "22E45",
      "17B65"
    ],
    "keywords": [
      "unitary representation",
      "frechet-lie supergroups",
      "locally convex lie group",
      "lie algebra action",
      "trotter property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2639S"
    }
  }
}