{
  "annotation_id": "cf714841-727f-4730-805b-c5a73ed52a16",
  "date_created": "2026-03-02T18:01:27.680000Z",
  "date_modified": "2026-03-02T18:01:27.680000Z",
  "file_hash": "78e437285e535c6ff18f96ba91c7aa5339fb4200931208fcb5b85c89c9614031",
  "private": false,
  "record": {
    "abstract": "Let X=GM be a finite group factorisation. It is shown that the quantum double\nD(H) of the associated bicrossproduct Hopf algebra $H=kM\\cobicross k(G)$ is\nitself a bicrossproduct $kX\\cobicross k(Y)$ associated to a group YX, where\n$Y=G\\times M^{op}$. This provides a class of bicrossproduct Hopf algebras which\nare quasitriangular. We also construct a subgroup $Y^\\theta X^\\theta$\nassociated to every order-reversing automorphism $\\theta$ of X. The\ncorresponding Hopf algebra $kX^\\theta\\cobicross k(Y^\\theta)$ has the same\ncoalgebra as H. Using related results, we classify the first order bicovariant\ndifferential calculi on H in terms of orbits in a certain quotient space of X.",
    "arxiv_id": "q-alg/9701041",
    "authors": [
      "E. Beggs",
      "S. Majid"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Quasitriangular and differential structures on bicrossproduct Hopf   algebras",
    "url": "https://arxiv.org/abs/q-alg/9701041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c202e11a-be4b-4bed-9d86-bb453b230260",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}