{
  "annotation_id": "56cc812a-c554-4673-8453-89257ca9bb40",
  "date_created": "2026-03-02T18:01:28.406000Z",
  "date_modified": "2026-03-02T18:01:28.406000Z",
  "file_hash": "af4d4a7dc0273ed1a3e77b57d55d57f49ef1fdda82912f0d9d7005affceb4a62",
  "private": false,
  "record": {
    "abstract": "We consider a pair of independent scalar products, one scalar product on\nvectors, and another independent scalar product on dual space of co-vectors.\nThe Clifford co-product of multivectors is calculated from the dual Clifford\nalgebra. With respect to this co-product unit is not group-like and vectors are\nnot primitive. The Clifford product and the Clifford co-product fits to the\nbi-gebra with respect to the family of the (pre)-braids. The Clifford bi-gebra\nis in a braided category iff at least one of these scalar products vanish.",
    "arxiv_id": "q-alg/9709016",
    "authors": [
      "Zbigniew Oziewicz"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1023/A:1022833801475",
    "journal_ref": "Czechoslovak Journal of Physics Vol. 47 (12) (1997) 1267-1274",
    "title": "Clifford Hopf-gebra and Bi-universal Hopf-gebra",
    "url": "https://arxiv.org/abs/q-alg/9709016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55aa63e9-6e27-4da8-979b-e21a1011b58a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}