{
  "annotation_id": "d6ab07cb-1661-472f-91ce-48939b907a6b",
  "date_created": "2026-03-02T18:01:24.726000Z",
  "date_modified": "2026-03-02T18:01:24.726000Z",
  "file_hash": "d27f7346168f187853bdb77023ef7b7a779f18f8714bc277518b00cb64d822a7",
  "private": false,
  "record": {
    "abstract": "We show that bicovariant bimodules as defined by Woronowicz are in one to one\ncorrespondence with the Drinfeld quantum double representations. We then prove\nthat a differential calculus associated to a bicovariant bimodule of dimension\nn is connected to the existence of a particular (n+1)--dimensional\nrepresentation of the double. An example of bicovariant differential calculus\non the non quasitriangular quantum group E_q(2) is developed. The construction\nis studied in terms of Hochschild cohomology and a correspondence between\ndifferential calculi and 1-cocycles is proved. Some differences of calculi on\nquantum and finite groups with respect to Lie groups are stressed.",
    "arxiv_id": "q-alg/9507004",
    "authors": [
      "F. Bonechi",
      "R. Giachetti",
      "R. Maciocco",
      "E. Sorace",
      "M. Tarlini"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/BF00312672",
    "title": "Quantum Double and Differential Calculi",
    "url": "https://arxiv.org/abs/q-alg/9507004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1633243d-a048-4ea2-b190-bee9c17f9799",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}