{
  "annotation_id": "eb07e765-63c2-4816-9389-5674ba6c5a76",
  "date_created": "2026-03-02T18:01:25.403000Z",
  "date_modified": "2026-03-02T18:01:25.403000Z",
  "file_hash": "69370dc1aebecf57a570eaaf9bdfba6f993b99890cf263b2f99acadf18b96ee0",
  "private": false,
  "record": {
    "abstract": "We investigate the possibility to construct bicovariant differential calculi\non quantum groups SO_q(N) and Sp_q(N) as a quantization of an underlying\nbicovariant bracket.We show that, opposite to GL(N) and SL(N)-cases, neither of\npossible graded SO- and Sp- bicovariant brackets (associated with a\nquasitriangular r-matrices) obey the Jacobi identity when the differential\nforms are Lie algebra- valued. The absence of a classical Poisson structure\ngives an indication that differential algebras describing bicovariant\ndifferential calculi on quantum orthogonal and symplectic groups are not of\nPoincar\u0027e- Birkhoff- -Witt type.",
    "arxiv_id": "q-alg/9502002",
    "authors": [
      "G. E. Arutuynov",
      "A. P. Isaev",
      "Z. Popowicz"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/28/15/015",
    "journal_ref": "J.Phys.A28:4349-4359,1995",
    "title": "Poincare\u0027-Birkhoff-Witt property for bicovariant differential algebras   on simple quantum groups",
    "url": "https://arxiv.org/abs/q-alg/9502002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1a70d7a9-3eb2-4193-b6c6-f70523082e4d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}