{
  "annotation_id": "bb88c32f-b570-4a23-a927-ec8e737e00d5",
  "date_created": "2026-03-02T18:01:28.710000Z",
  "date_modified": "2026-03-02T18:01:28.710000Z",
  "file_hash": "bb8fc5d2bc5b48a232c5456bc66ca60dc6c19212e85fdc0115b6f7a404c31891",
  "private": false,
  "record": {
    "abstract": "We consider Hopf bimodules and crossed modules over a Hopf algebra $H$ in a\nbraided category. They are the key-stones for braided bicovariant differential\ncalculi and their invariant vector fields respectively, as well as for the\nconstruction of braided Hopf algebra cross products. We show that the notions\nof Hopf bimodules and crossed modules are equivalent. A generalization of the\nRadford-Majid criterion to the braided case is given and it is seen that\nbialgebra cross products over the Hopf algebra $H$ are precisely described by\n$H$-crossed module bialgebras. We study the theory of (bicovariant)\ndifferential calculi in braided abelian categories and we construct\n$\\NN_0$-graded bicovariant differential calculi out of first order bicovariant\ndifferential calculi. These objects are shown to be Hopf algebra differential\ncalculi with universal bialgebra properties in the braided $\\NN_0$-graded\ncategory.",
    "arxiv_id": "q-alg/9608019",
    "authors": [
      "Yuri Bespalov",
      "Bernhard Drabant"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Bicovariant Differential Calculi and Cross Products on Braided Hopf   Algebras",
    "url": "https://arxiv.org/abs/q-alg/9608019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8f3afdf6-7146-4be6-b9c7-13dcde9f0362",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}