{
  "id": "0906.2362",
  "version": "v1",
  "published": "2009-06-12T15:37:22.000Z",
  "updated": "2009-06-12T15:37:22.000Z",
  "title": "A New Characterisation of Idempotent States on Finite and Compact Quantum Groups",
  "authors": [
    "Uwe Franz",
    "Adam Skalski"
  ],
  "comment": "9 pages",
  "journal": "Comptes Rendus Mathematique Vol. 347, pp. 991-996, 2009",
  "doi": "10.1016/j.crma.2009.06.015",
  "categories": [
    "math.OA",
    "math.QA"
  ],
  "abstract": "We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idempotent states on a finite quantum group and by its coidalgebras are isomorphic. We show furthermore that these lattices are also isomorphic for compact quantum groups, if one restricts to expected coidalgebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-12T15:37:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "43A05",
      "46L65"
    ],
    "keywords": [
      "compact quantum groups",
      "idempotent states",
      "finite quantum groups correspond",
      "characterisation",
      "isomorphic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2362F"
    }
  }
}