{
  "annotation_id": "c5dd52e4-9ec4-4267-93de-f3bf258acaa2",
  "date_created": "2026-03-02T18:01:21.619000Z",
  "date_modified": "2026-03-02T18:01:21.619000Z",
  "file_hash": "2bc44975beb3d4fe5ccc4be12c2d0acccd0f8c2eb14d593c82d33f8ef5b627b9",
  "private": false,
  "record": {
    "abstract": "N-Lie algebra structures on smooth function algebras given by means of\nmulti-differential operators, are studied. Necessary and sufficient conditions\nfor the sum and the wedge product of two $n$-Poisson sructures to be again a\nmulti-Poisson are found. It is proven that the canonical $n$-vector on the dual\nof an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The\nproblem of compatibility of two n-Lie algebra structures is analyzed and the\ncompatibility relations connecting hereditary structures of a given n-Lie\nalgebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their\n\"elementary particle-like\" structure is discovered. Some simple applications to\ndynamics are discussed.",
    "arxiv_id": "physics/9709046",
    "authors": [
      "G. Marmo",
      "G. Vilasi",
      "A. Vinogradov"
    ],
    "categories": [
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0393-0440(97)00057-0",
    "journal_ref": "J.Geom.Phys.25:141-182,1998",
    "title": "The local structure of n-Poisson and n-Jacobi manifolds",
    "url": "https://arxiv.org/abs/physics/9709046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "121a5870-8de4-44c4-8dd2-f19ad335c7b4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}