{
  "annotation_id": "ecd6bbf3-75d0-4660-bfb1-e11c1a37c456",
  "date_created": "2026-03-02T18:01:28.815000Z",
  "date_modified": "2026-03-02T18:01:28.815000Z",
  "file_hash": "96bb362a7a4ec730152c8b08130af94822c29fc7336d27110133290b43f70562",
  "private": false,
  "record": {
    "abstract": "The set of primitive elements of a Hopf algebra in the braided category of\ngroup graded vector spaces (with a commutative group) carry the structure of a\ngeneralized Lie algebra. In particular the graded derivations of an associative\nalgebra carry this Lie algebra structure. The Lie multiplications consist of\ncertain n-ary partially defined multiplications satisfying generalized\nantisymmetry and Jacobi identities. This generalizes the concept of Lie super\nalgebras and Lie color algebras.\n  We show that universal enveloping algebras in the braided category exist.\nThey are (braided) Hopf algebras. This explains many constructions of\nnoncommutative noncocommutative Hopf algebras in the literature.",
    "arxiv_id": "q-alg/9612002",
    "authors": [
      "Bodo Pareigis"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "On Lie Algebras in Braided Categories",
    "url": "https://arxiv.org/abs/q-alg/9612002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6416ddb8-cabe-40ce-bac7-d1a25fbb9d09",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}