{
  "id": "math/0012037",
  "version": "v1",
  "published": "2000-12-06T11:20:08.000Z",
  "updated": "2000-12-06T11:20:08.000Z",
  "title": "An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center",
  "authors": [
    "Hellmut Baumgaertel",
    "Fernando Lledo"
  ],
  "comment": "10 pages, Latex2e",
  "journal": "Fields Inst.Commun. 30 (2001) 1-10",
  "categories": [
    "math.OA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains characteristic mutually isomorphic subcategories of the Doplicher/Roberts-type which are connected with the choice of distinguished G-invariant algebraic Hilbert spaces within the corresponding G-invariant Hilbert Z-modules. We present in this paper the solution of the corresponding inverse problem. More precisely, assuming that the given endomorphism category T of a C*-algebra A with center Z contains a certain subcategory of the DR-type, a Hilbert extension {F,G} of A is constructed such that T is isomorphic to the category of all canonical endomorphisms of A w.r.t. {F,G} and A'\\cap F=Z. Furthermore, there is a natural equivalence relation between admissible subcategories and it is shown that two admissible subcategories yield A-module isomorphic Hilbert extensions iff they are equivalent. The essential step of the solution is the application of the standard DR-theory to the assigned subcategory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-12-06T11:20:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47L65",
      "22D25",
      "46L08"
    ],
    "keywords": [
      "nontrivial center",
      "endomorphism category",
      "dr-duality theory",
      "a-module isomorphic hilbert extensions",
      "g-invariant algebraic hilbert spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 642038,
      "adsabs": "2000math.....12037B"
    }
  }
}