{
  "annotation_id": "3d2691e2-a426-45d6-b474-19f8c2846de1",
  "date_created": "2026-03-02T18:01:24.712000Z",
  "date_modified": "2026-03-02T18:01:24.712000Z",
  "file_hash": "b651dce3e5deffe525a5592c27b571d6e1b785a46ef99f18e1f9e3fa73655f85",
  "private": false,
  "record": {
    "abstract": "We compute the quantum double, braiding and other canonical Hopf algebra\nconstructions for the bicrossproduct Hopf algebra $H$ associated to the\nfactorization of a finite group into two subgroups. The representations of the\nquantum double are described by a notion of bicrossed bimodules, generalising\nthe cross modules of Whitehead. We also show that self-duality structures for\nthe bicrossproduct Hopf algebras are in one-one correspondence with\nfactor-reversing group isomorphisms. The example $Z_6Z_6$ is given in detail.\n  We show further that the quantum double $D(H)$ is the twisting of $D(X)$ by a\nnon-trivial quantum cocycle, where $X$ is the associated double cross product\ngroup.",
    "arxiv_id": "q-alg/9503018",
    "authors": [
      "E. Beggs",
      "J. Gould",
      "S. Majid"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Finite Group Factorisations and Braiding",
    "url": "https://arxiv.org/abs/q-alg/9503018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6be3da2f-4dc4-4c5f-8f35-dcb87e7696d1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}