{
  "id": "2407.19314",
  "version": "v1",
  "published": "2024-07-27T18:10:02.000Z",
  "updated": "2024-07-27T18:10:02.000Z",
  "title": "Tracial central states on compact quantum groups",
  "authors": [
    "Amaury Freslon",
    "Adam Skalski",
    "Simeng Wang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.OA",
    "math.QA"
  ],
  "abstract": "Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study tracial central states on universal C*-algebras associated with compact quantum groups, where centrality is understood in the sense of invariance under the adjoint action. We fully classify such states on $q$-deformations of compact Lie groups, on free orthogonal quantum groups, quantum permutation groups and on quantum hyperoctahedral groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-27T18:10:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact quantum groups",
      "free orthogonal quantum groups",
      "study tracial central states",
      "conjugation invariant positive-definite functions",
      "quantum hyperoctahedral groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}