{
  "annotation_id": "6858a6b0-d9fe-4ca1-a339-174a03250abc",
  "date_created": "2026-03-02T18:01:28.713000Z",
  "date_modified": "2026-03-02T18:01:28.713000Z",
  "file_hash": "02172b6d9ad2fb86ed391525e1ddac81fd2398df50ce460359924ca72cef695f",
  "private": false,
  "record": {
    "abstract": "We present some results concerning the generalized homologies associated with\nnilpotent endomorphisms $d$ such that $d^N=0$ for some integer $N\\geq 2$. We\nthen introduce the notion of graded $q$-differential algebra and describe some\nexamples. In particular we construct the $q$-analog of the simplicial\ndifferential on forms, the $q$-analog of the Hochschild differential and the\n$q$-analog of the universal differential envelope of an associative unital\nalgebra.",
    "arxiv_id": "q-alg/9609012",
    "authors": [
      "Michel Dubois-Violette"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/BF01690337",
    "title": "Generalized differential spaces with $d^N=0$ and the $q$-differential   calculus",
    "url": "https://arxiv.org/abs/q-alg/9609012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "50dc8a70-8b0e-4cad-9892-64b6fa55c478",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}