{
  "annotation_id": "70a473fe-7635-46ea-a697-4da336d76c8c",
  "date_created": "2026-03-02T18:01:28.524000Z",
  "date_modified": "2026-03-02T18:01:28.524000Z",
  "file_hash": "4ec716ce362ebfa03bb5203e0647e66b0a45d8779b18b69d49fb114cd230bba8",
  "private": false,
  "record": {
    "abstract": "It is shown that the elliptic algebra ${\\cal A}_{q,p}(\\hat{sl}(2)_c)$ at the\ncritical level c=-2 has a multidimensional center containing some trace-like\noperators t(z). A family of Poisson structures indexed by a non-negative\ninteger and containing the q-deformed Virasoro algebra is constructed on this\ncenter. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m\ninteger, they commute when in addition p=q^{2k} for k integer non-zero, and\nthey belong to the center of ${\\cal A}_{q,p}(\\hat{sl}(2)_c)$ when k is odd. The\nPoisson structures obtained for t(z) in these classical limits contain the\nq-deformed Virasoro algebra, characterizing the structures at generic values of\np, q and m as new ${\\cal W}_{q,p}(sl(2))$ algebras.",
    "arxiv_id": "q-alg/9707034",
    "authors": [
      "J. Avan",
      "L. Frappat",
      "M. Rossi",
      "P. Sorba"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1023/A:1021645814342",
    "title": "From quantum to elliptic algebras",
    "url": "https://arxiv.org/abs/q-alg/9707034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2d327df2-e308-438e-accc-b4cf6a0676df",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}