{
  "id": "math/0504362",
  "version": "v1",
  "published": "2005-04-18T14:46:41.000Z",
  "updated": "2005-04-18T14:46:41.000Z",
  "title": "Abelian subalgebras of von Neumann algebras from flat tori in locally symmetric spaces",
  "authors": [
    "Guyan Robertson"
  ],
  "journal": "J. Funct. Anal., 230 (2006), 419-431",
  "categories": [
    "math.OA",
    "math.DG"
  ],
  "abstract": "Consider a compact locally symmetric space $M$ of rank $r$, with fundamental group $\\Gamma$. The von Neumann algebra $\\vn(\\Gamma)$ is the convolution algebra of functions $f\\in\\ell_2(\\Gamma)$ which act by left convolution on $\\ell_2(\\Gamma)$. Let $T^r$ be a totally geodesic flat torus of dimension $r$ in $M$ and let $\\Gamma_0\\cong\\bb Z^r$ be the image of the fundamental group of $T^r$ in $\\Gamma$. Then $\\vn(\\Gamma_0)$ is a maximal abelian $\\star$-subalgebra of $\\vn(\\Gamma)$ and its unitary normalizer is as small as possible. If $M$ has constant negative curvature then the Puk\\'anszky invariant of $\\vn(\\Gamma_0)$ is $\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-18T14:46:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D25",
      "22E40"
    ],
    "keywords": [
      "von neumann algebra",
      "abelian subalgebras",
      "fundamental group",
      "totally geodesic flat torus",
      "compact locally symmetric space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4362R"
    }
  }
}