{
  "annotation_id": "4072c6ab-3db5-48b1-8ad5-a823ede1cba1",
  "date_created": "2026-03-02T18:01:24.711000Z",
  "date_modified": "2026-03-02T18:01:24.711000Z",
  "file_hash": "c33138778faa06c195f92ef16bb7d0915c09d5a47ef3f015fd40cc1e36a3ea75",
  "private": false,
  "record": {
    "abstract": "We introduce the notion of Hopf algebroids, in which neither the total\nalgebras nor the base algebras are required to be commutative. We give a class\nof Hopf algebroids associated to module algebras of the Drinfeld doubles of\nHopf algebras when the $R$-matrices act properly. When this construction is\napplied to quantum groups, we get examples of quantum groupoids, which are\nsemi-classical limits of Poisson groupoids. The example of quantum $sl(2)$ is\nworked out in details.",
    "arxiv_id": "q-alg/9505024",
    "authors": [
      "Jiang-Hua Lu"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Hopf algebroids and quantum groupoids",
    "url": "https://arxiv.org/abs/q-alg/9505024"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1b687d43-8062-40bf-b91c-7311814e577a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}