{
  "annotation_id": "e6ffea2f-75c9-4bbe-bc58-132f46cd02fc",
  "date_created": "2026-03-02T18:01:24.723000Z",
  "date_modified": "2026-03-02T18:01:24.723000Z",
  "file_hash": "9c56b9b24f77af6366a97363fefcb731f959d8eb3b4fcc6d1ec21fa606d0f9ab",
  "private": false,
  "record": {
    "abstract": "As a natural generalization of ordinary Lie algebras we introduce the concept\nof quantum Lie algebras ${\\cal L}_q(g)$. We define these in terms of certain\nadjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a\nquantum Lie bracket given by the quantum adjoint action. The structure\nconstants of these algebras depend on the quantum deformation parameter $q$ and\nthey go over into the usual Lie algebras when $q=1$.\n  The notions of q-conjugation and q-linearity are introduced. q-linear\nanalogues of the classical antipode and Cartan involution are defined and a\ngeneralised Killing form, q-linear in the first entry and linear in the second,\nis obtained. These structures allow the derivation of symmetries between the\nstructure constants of quantum Lie algebras.\n  The explicitly worked out examples of $g=sl_3$ and $so_5$ illustrate the\nresults.",
    "arxiv_id": "q-alg/9506017",
    "authors": [
      "Gustav W. Delius",
      "Andreas Hueffmann"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/29/8/018",
    "journal_ref": "J.Phys.A29:1703-1722,1996",
    "title": "On Quantum Lie Algebras and Quantum Root Systems",
    "url": "https://arxiv.org/abs/q-alg/9506017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8cfb4f68-5470-47cf-b5dc-5aefb160e8d6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}