{
  "annotation_id": "16009e9e-8298-4f4c-9913-51202acd1f94",
  "date_created": "2026-03-02T18:01:28.658000Z",
  "date_modified": "2026-03-02T18:01:28.658000Z",
  "file_hash": "475e9de2f64104ca487c830e76d108c24236f11080257cc1d362f27a2d0c51e1",
  "private": false,
  "record": {
    "abstract": "Let $\\Gamma$ be an $N^2$-dimensional bicovariant first order differential\ncalculus on a Hopf algebra $SL_q(N)$. There are three possibilities to\nconstruct a differential Z-graded Hopf algebra $\\Gamma^\\wedge$ which contains\n$\\Gamma$ as its first order part. Let $q$ be a transcendental complex number.\nFor $N\u003e2$ these three Z-graded Hopf algebras coincide. For Woronowicz\u0027 external\nalgebra we calculate the dimensions of the spaces of left-invariant and\nbi-invariant $k$-forms. In this case each bi-invariant form is closed. In case\nof $4D_\\pm$ calculi on $SL_q(2)$ the universal calculus is strictly larger than\nthe other two calculi. In particular, the bi-invariant 1-form is not closed.",
    "arxiv_id": "q-alg/9708013",
    "authors": [
      "I. Heckenberger",
      "A. Schueler"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1023/A:1021614302046",
    "title": "Higher Order Differential Calculus on $SL_q(N)$",
    "url": "https://arxiv.org/abs/q-alg/9708013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6fefa3bd-354c-4dec-bc5e-9447b41373a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}