{
  "annotation_id": "5d90bfb7-17f5-46ad-a19e-48d208985d3e",
  "date_created": "2026-03-02T18:01:27.602000Z",
  "date_modified": "2026-03-02T18:01:27.602000Z",
  "file_hash": "b73ee0a4f23b091b60410872fd65950eb3bf70af84058e43142ec61321876a30",
  "private": false,
  "record": {
    "abstract": "Quantum Lie algebras are generalizations of Lie algebras which have the\nquantum parameter h built into their structure. They have been defined\nconcretely as certain submodules of the quantized enveloping algebras. On them\nthe quantum Lie bracket is given by the quantum adjoint action.\n  Here we define for any finite-dimensional simple complex Lie algebra g an\nabstract quantum Lie algebra g_h independent of any concrete realization. Its\nh-dependent structure constants are given in terms of inverse quantum\nClebsch-Gordan coefficients. We then show that all concrete quantum Lie\nalgebras are isomorphic to an abstract quantum Lie algebra g_h.\n  In this way we prove two important properties of quantum Lie algebras: 1) all\nquantum Lie algebras associated to the same g are isomorphic, 2) the quantum\nLie bracket of any quantum Lie algebra is $q$-antisymmetric. We also describe a\nconstruction of quantum Lie algebras which establishes their existence.",
    "arxiv_id": "q-alg/9605025",
    "authors": [
      "Gustav W. Delius",
      "Mark D. Gould"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/s002200050107",
    "journal_ref": "Commun. Math. Phys. 185, 709-722 (1997)",
    "title": "Quantum Lie algebras; their existence, uniqueness and $q$-antisymmetry",
    "url": "https://arxiv.org/abs/q-alg/9605025"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e27abc22-9eb8-476e-8217-4478d3a3412b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}