{
  "annotation_id": "77903dff-a83c-41c2-aa11-4826240871de",
  "date_created": "2026-03-02T18:02:51.355000Z",
  "date_modified": "2026-03-02T18:02:51.355000Z",
  "file_hash": "53ea88a07ac2953d93b9e4203e1befc85e1c19c2a40987bcf50d57cd676a2e78",
  "private": false,
  "record": {
    "abstract": "The symmetry algebra $P_\\infty = W_\\infty \\oplus H \\oplus I_\\infty$ of\nintegrable systems is defined. As an example the classical Sophus Lie point\nsymmetries of all higher KP equations are obtained. It is shown that one\n(``positive\u0027\u0027) half of the point symmetries belongs to the $W_\\infty$\nsymmetries while the other (``negative\u0027\u0027) part belongs to the $I_\\infty$ ones.\nThe corresponing action on the tau-function is obtained for the positive part\nof the symmetries. The negative part can not be obtained from the free fermion\nalgebra. A new embedding of the Virasoro algebra into $gl(\\infty )$n describes\nconformal transformations of the KP time variables. A free fermion algebra\ncocycle is described as a PDO Lie algebra cocycle.",
    "arxiv_id": "solv-int/9701008",
    "authors": [
      "A. Yu. Orlov",
      "P. Winternitz"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1142/S0217979297001532",
    "title": "$P_\\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra   of pseudodifferential operators",
    "url": "https://arxiv.org/abs/solv-int/9701008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ba91b022-f52f-4dd5-9e5e-5408bb766662",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}