{
  "id": "1607.07830",
  "version": "v1",
  "published": "2016-07-26T18:25:23.000Z",
  "updated": "2016-07-26T18:25:23.000Z",
  "title": "Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups",
  "authors": [
    "Adrien Boyer"
  ],
  "categories": [
    "math.GR",
    "math.OA",
    "math.RT"
  ],
  "abstract": "We prove that the Harish-Chandra--Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced $C^*$-algebra of the discrete subgroup. Then, we prove that for the reduced $C^*$-norm is controlled by the norm of the Harish-Chandra--Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properly on a Riemannian symmetric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-26T18:25:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semisimple lie group",
      "discrete subgroup",
      "harish-chandra-schwartzs algebras",
      "harish-chandra-schwartz space",
      "riemannian symmetric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}