{
  "annotation_id": "32a21622-a8c6-4f65-bccb-19014bb9c0c2",
  "date_created": "2026-03-02T18:01:27.740000Z",
  "date_modified": "2026-03-02T18:01:27.740000Z",
  "file_hash": "afb968c5885b1e14543432abf108bb8626b33c3bb3184a4cb02752a6e42bee87",
  "private": false,
  "record": {
    "abstract": "Let $ \\mathfrak{g} $ be an untwisted affine Kac-Moody algebra over the field\n$ K \\, $, and let $ U_q(\\mathfrak{g}) $ be the associated quantum enveloping\nalgebra; let $ \\mathfrak{U}_q(g) $ be the Lusztig\u0027s integer form of $\nU_q(\\mathfrak{g}) \\, $, generated by $ q $-divided powers of Chevalley\ngenerators over a suitable subring $ R $ of $ K(q) \\, $. We prove a\nPoincar\\\u0027e-Birkhoff-Witt like theorem for $ \\mathfrak{U}_q(\\mathfrak{g}) \\, $,\nyielding a basis over $ R $ made of ordered products of $ q $-divided powers of\nsuitable quantum root vectors.",
    "arxiv_id": "q-alg/9706018",
    "authors": [
      "Fabio Gavarini"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1080/00927879908826468",
    "journal_ref": "Communications in Algebra 27, no. 2 (1999), 903-918",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A PBW basis for Lusztig\u0027s form of untwisted affine quantum groups",
    "url": "https://arxiv.org/abs/q-alg/9706018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2f49aaa0-bef1-4d81-a0c8-e0fa3ed690af",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}