{
  "annotation_id": "812cbf35-af6b-4002-9c03-1ecdbaf9dc86",
  "date_created": "2026-03-02T18:01:24.967000Z",
  "date_modified": "2026-03-02T18:01:24.967000Z",
  "file_hash": "767013ef214028371c7d951a3459d8c081de7d61adcfd0cc94fb1dfd777fb5e0",
  "private": false,
  "record": {
    "abstract": "A large family of \"standard\" coboundary Hopf algebras is investigated. The\nexistence of a universal R-matrix is demonstrated for the case when the\nparameters are in general position. Special values of the parameters are\ncharacterized by the appearance of certain ideals; in this case the universal\nR-matrix exists on the associated algebraic quotient. In special cases the\nquotient is a \"standard\" quantum group; all familiar quantum groups including\ntwisted ones are obtained in this way. In other special cases one finds new\ntypes of coboundary bi-algebras. A large class of first order deformations of\nall these standard bi-algebras is investigated and the associated deformed\nuniversal R-matrices have been calculated. One obtains, in particular,\nuniversal R-matrices associated with all simple, complex Lie algebras\n(classification by Belavin and Drinfeld) to first order in the deformation\nparameter.",
    "arxiv_id": "q-alg/9510002",
    "authors": [
      "C. Fr\u00f8nsdal"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Generalization and Deformations of Quantum Groups; Quantization of All   Simple Lie Bi-Algebras",
    "url": "https://arxiv.org/abs/q-alg/9510002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c685e244-f07a-4357-a322-08796ae43421",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}