{
  "annotation_id": "73ca771b-73c9-42f6-b21f-fa07b03a71d9",
  "date_created": "2026-03-02T18:01:28.702000Z",
  "date_modified": "2026-03-02T18:01:28.702000Z",
  "file_hash": "a3f4311018b2593cd0ea0ae0ba4e000bad68bcdf976456878387ebf3ce6166b2",
  "private": false,
  "record": {
    "abstract": "From the bicovariant first order differential calculus on inhomogeneous Hopf\nalgebra ${\\cal B}$ we construct the set of right-invariant Maurer-Cartan\none-forms considered as a right-invariant basis of a bicovariant ${\\cal\nB}$-bimodule over which we develop the Woronowicz\u0027s general theory of\ndifferential calculus on quantum groups. In this formalism, we introduce\nsuitable functionals on ${\\cal B}$ which control the inhomogeneous commutation\nrules. In particular we find that the homogeneous part of commutation rules\nbetween the translations and those between the generators of the homogeneous\npart of ${\\cal B}$ and translations are controled by different R-matrices\nsatisfying nontrivial characteristic equations.",
    "arxiv_id": "q-alg/9705005",
    "authors": [
      "M. Lagraa",
      "N. Touhami"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "title": "The Noncommutative Inhomogeneous Hopf Algebra",
    "url": "https://arxiv.org/abs/q-alg/9705005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a129aa59-c4f0-4b89-a61b-dda3168eb483",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}