{
  "annotation_id": "8b649263-1d37-46dc-b4b8-7448aaefb134",
  "date_created": "2026-03-02T18:01:24.708000Z",
  "date_modified": "2026-03-02T18:01:24.708000Z",
  "file_hash": "de9cde33f1c676b6a3eda750626fbe80e6d9e490ee02eb5d31d214174ff7b140",
  "private": false,
  "record": {
    "abstract": "In this paper we introduce two classes of Poisson brackets on algebras (or on\nsheaves of algebras). We call them locally free and nonsingular Poisson\nbrackets. Using the Fedosov\u0027s method we prove that any locally free nonsingular\nPoisson bracket can be quantized. In particular, it follows from this that all\nPoisson brackets on an arbitrary field of characteristic zero can be quantized.\nThe well known theorem about the quantization of nondegenerate Poisson brackets\non smooth manifolds follows from the main result of this paper as well.",
    "arxiv_id": "q-alg/9505028",
    "authors": [
      "J. Donin"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1006/aima.1997.1626",
    "journal_ref": "Advances in Mathematics Volume 127, Issue 1, 15 April 1997, Pages\n  73-93",
    "title": "On the quantization of Poisson brackets",
    "url": "https://arxiv.org/abs/q-alg/9505028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f27b302a-cbd8-40a8-9edb-08e10c722bfd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}