{
  "annotation_id": "7dd33590-1e29-46cc-baa9-6d229c2d55ae",
  "date_created": "2026-03-02T18:01:25.149000Z",
  "date_modified": "2026-03-02T18:01:25.149000Z",
  "file_hash": "b5e957a326249be9ad929e4da4a3a437c0b3ed291f67e077ca97a45a547e54e4",
  "private": false,
  "record": {
    "abstract": "Quadratic Poisson brackets on associative algebras are studied. Such a\nbracket compatible with the multiplication is related to a differentiation in\ntensor square of the underlying algebra. Jacobi identity means that this\ndifferentiation satisfies a classical Yang--Baxter equation. Corresponding Lie\ngroups are canonically equipped with a Poisson Lie structure. A way to quantize\nsuch structures is suggested.",
    "arxiv_id": "q-alg/9501019",
    "authors": [
      "A. A. Balinsky",
      "Yu. M. Burman"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Quadratic Poisson brackets and Drinfel\u0027d theory for associative algebras",
    "url": "https://arxiv.org/abs/q-alg/9501019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "682dd0dd-f501-4ec4-b648-772d48043ab7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}