{
  "annotation_id": "a9d4896a-f5a0-4039-8771-6b0e3a5f14a3",
  "date_created": "2026-03-02T18:01:27.737000Z",
  "date_modified": "2026-03-02T18:01:27.737000Z",
  "file_hash": "f0552d0664c8eec1a49c081b8838f31505a1e250952f4d6a1330dd5802f241da",
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  "record": {
    "abstract": "A proof of Poincar\\\u0027e-Birkhoff-Witt theorem is given for a class of\ngeneralized Lie algebras closely related to the Gurevich S-Lie algebras. As\nconcrete examples, we construct the positive (negative) parts of the quantized\nuniversal enveloping algebras of type A_n and M_{p,q,e}(n,K), which is a\nnon-standard quantum deformation of GL(n). In particular, we get, for both\nalgebras, a unified proof of the Poincar\\\u0027e-Birkhoff-Witt theorem and we show\nthat they are genuine universal enveloping algebras of certain generalized Lie\nalgebras.",
    "arxiv_id": "q-alg/9706016",
    "authors": [
      "Cesar Bautista"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1063/1.532471",
    "journal_ref": "J. Math. Phys. 39 (1998) 3828-3843",
    "title": "A Poincar\\\u0027e-Birkhoff-Witt theorem for generalized color Lie algebras",
    "url": "https://arxiv.org/abs/q-alg/9706016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f2cc18bf-bb57-45e0-9011-e44dd6e44660",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}