{
  "annotation_id": "a97585ca-2f0b-4d2b-b4dd-d2023f598afe",
  "date_created": "2026-03-02T18:01:28.712000Z",
  "date_modified": "2026-03-02T18:01:28.712000Z",
  "file_hash": "60b88cc8a622a47c26f369317929e42932292ae1700db8d921a1ea4150431b2c",
  "private": false,
  "record": {
    "abstract": "We define and investigate pairings of multiplier Hopf algebras. It is shown\nthat two dually paired regular multiplier Hopf ($*$-)algebras $A$ and $B$ yield\na quantum double multiplier Hopf ($*$-)algebra which is again regular.\nIntegrals on $A$ and $B$ induce an integral on the quantum double. The results\ngeneralize pairing and quantum double construction from ordinary Hopf algebras\nto multiplier Hopf algebras.",
    "arxiv_id": "q-alg/9609013",
    "authors": [
      "Bernhard Drabant",
      "Alfons Van Daele"
    ],
    "categories": [
      "q-alg",
      "funct-an",
      "math.FA",
      "math.QA"
    ],
    "title": "Pairing and Quantum Double of Multiplier Hopf Algebras",
    "url": "https://arxiv.org/abs/q-alg/9609013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "19a64652-7099-4b4a-bbfd-3b50ccccf27c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}