{
  "id": "2112.07506",
  "version": "v2",
  "published": "2021-12-14T16:11:08.000Z",
  "updated": "2022-02-10T15:00:03.000Z",
  "title": "Tannaka-Krein reconstruction and ergodic actions of easy quantum groups",
  "authors": [
    "Amaury Freslon",
    "Frank Taipe",
    "Simeng Wang"
  ],
  "comment": "45 pages. v2: minor changes; several improvements and corrections in Section 6",
  "categories": [
    "math.OA",
    "math.QA"
  ],
  "abstract": "We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to construct families of ergodic actions of easy quantum groups out of combinatorial data involving partitions and study them. Eventually, we use this categorical point of view to show that the quantum permutation group cannot act ergodically on a classical connected compact space, thereby answering a question of D. Goswami and H. Huang.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-10T15:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "05E10"
    ],
    "keywords": [
      "ergodic actions",
      "tannaka-krein reconstruction",
      "compact quantum groups",
      "quantum permutation group",
      "classical connected compact space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}