{
  "id": "math/0506276",
  "version": "v1",
  "published": "2005-06-14T14:06:02.000Z",
  "updated": "2005-06-14T14:06:02.000Z",
  "title": "Hilbert-Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry",
  "authors": [
    "Maria Gordina"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvature is $-\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-14T14:06:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58B20",
      "81R10"
    ],
    "keywords": [
      "infinite-dimensional lie groups",
      "hilbert-schmidt groups",
      "riemannian geometry",
      "ricci curvature",
      "infinite-dimensional lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6276G"
    }
  }
}