{
  "annotation_id": "2546e2c8-5bab-4bc3-a911-8ffa144b1f0b",
  "date_created": "2026-03-02T18:01:28.471000Z",
  "date_modified": "2026-03-02T18:01:28.471000Z",
  "file_hash": "3c912936db3c4556d1ab6c8d71ee9313ab9ea75475a85cf77e35a526ef75f2b5",
  "private": false,
  "record": {
    "abstract": "We introduce the notion of a crossed product of an algebra by a coalgebra\n$C$, which generalises the notion of a crossed product by a bialgebra\nwell-studied in the theory of Hopf algebras. The result of such a crossed\nproduct is an algebra which is also a right $C$-comodule. We find the necessary\nand sufficient conditions for two coalgebra crossed products be equivalent. We\nshow that the two-dimensional quantum Euclidean group is a coalgebra crossed\nproduct. The paper is completed with an appendix describing the dualisation of\nconstruction of coalgebra crossed products.",
    "arxiv_id": "q-alg/9603016",
    "authors": [
      "Tomasz Brzezinski"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Crossed Products by a Coalgebra",
    "url": "https://arxiv.org/abs/q-alg/9603016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "634628ea-3e82-41bc-b8b4-967f30e76b25",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}