{
  "annotation_id": "40843023-a652-4105-8bc2-6a4a85bf0618",
  "date_created": "2026-03-02T18:01:24.717000Z",
  "date_modified": "2026-03-02T18:01:24.717000Z",
  "file_hash": "eb9e89da3c9f558d68ec29e808b93349a265071b1f8c212458bfc477d5e85f58",
  "private": false,
  "record": {
    "abstract": "This work is motivated by a result of Drinfeld on Poisson homogeneous spaces.\nFor each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$,\nwe describe a Lie algebroid structure on the direct sum vector bundle $P \\times\n{\\frak g} \\oplus T^*P$, where ${\\frak g}$ is the Lie algebra of $G$. It is\nbuilt out of the transformation Lie algebroid $P \\times {\\frak g}$ and the\ncotangent bundle Lie algebroid $T^*P$ together with a pair of representations\nof them on each other. When the action of $G$ on $P$ is transitive, the kernel\nof the anchor map of this Lie algebroid gives a Lie algebra bundle over $P$,\nthe fibers of which are given by Drinfeld. As applications, we describe the\nsymplectic leaves and the $G$-invariant Poisson cohomology of Poisson\nhomogeneous $G$-spaces.",
    "arxiv_id": "q-alg/9503003",
    "authors": [
      "Jiang-Hua Lu"
    ],
    "categories": [
      "q-alg",
      "dg-ga",
      "math.DG",
      "math.QA"
    ],
    "title": "Lie Algebroids Associated to Poisson Actions",
    "url": "https://arxiv.org/abs/q-alg/9503003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8eeb97b9-55d0-4934-9a30-5a5a18515192",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}