{
  "annotation_id": "290dbe7d-bfee-4243-989d-344ab75957ac",
  "date_created": "2026-03-02T18:01:27.667000Z",
  "date_modified": "2026-03-02T18:01:27.667000Z",
  "file_hash": "a81d8766748b1e8292800ce0b505dda3064985b2a1bbbf910533b45b9cbe9964",
  "private": false,
  "record": {
    "abstract": "The category of Yetter-Drinfeld modules over a Hopf algebra (with bijektive\nantipode over a field) is a braided monoidal category. Given a Hopf algebra in\nthis category then the primitive elements of this Hopf algebra do not form an\nordinary Lie algebra anymore.\n  We introduce the notion of a (generalized) Lie algebra in the category of\nYetter-Drinfeld modules such that the set of primitive elements of a Hopf\nalgebra is a Lie algebra in this sense. It has n-ary partially defined Lie\nmultiplications on certain symmetric submodules of n- fold tensor products.\nThey satisfy antisymmetry and Jacobi identities. Also the Yetter-Drinfeld\nmodule of derivations of an associative algebra in the category of Yetter-\nDrinfeld modules is a Lie algebra. Furthermore for each Lie algebra in the\ncategory of Yetter-Drinfeld modules there is a universal enveloping algebra\nwhich turns out to be a (braided) Hopf algebra in this category.",
    "arxiv_id": "q-alg/9612023",
    "authors": [
      "Bodo Pareigis"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "On Lie Algebras in the Category of Yetter-Drinfeld Modules",
    "url": "https://arxiv.org/abs/q-alg/9612023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b3668ad9-8d39-4504-a835-73b958b635f9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}