{
  "annotation_id": "3e0492ac-26f7-46a4-b612-b20910923df0",
  "date_created": "2026-03-02T18:01:27.664000Z",
  "date_modified": "2026-03-02T18:01:27.664000Z",
  "file_hash": "026ec22261551ea08d0b2cff5383ed3d6e830bf6e226fbf13bd72b15e5f35a39",
  "private": false,
  "record": {
    "abstract": "We give a natural definition of a Poisson Differential Algebra. Consistence\nconditions are formulated in geometrical terms. It is found that one can often\nlocally put the Poisson structure on differential calculus in a simple\ncanonical form by a coordinate transformation. This is in analogy with the\nstandard Darboux\u0027s theorem for symplectic geometry. For certain cases there\nexists a realization of the exterior derivative through a certain canonical\none-form. All the above are carried out similarly for the case of a complex\nPoisson Differential Algebra. The case of one complex dimension is treated in\ndetails and interesting features are noted. A conclusion is made in the last\nsection.",
    "arxiv_id": "q-alg/9612031",
    "authors": [
      "Chong-Sun Chu",
      "Pei-Ming Ho"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1142/S0217751X97002929",
    "journal_ref": "Int.J.Mod.Phys. 12 (1997) 5573-5587",
    "title": "Poisson Algebra of Differential Forms",
    "url": "https://arxiv.org/abs/q-alg/9612031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "94f95e31-9ca8-45f1-99ea-2964cdaa29a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}