{
  "annotation_id": "e8bdc493-7150-4d71-b5b8-1820e1ab23a5",
  "date_created": "2026-03-02T18:01:28.483000Z",
  "date_modified": "2026-03-02T18:01:28.483000Z",
  "file_hash": "57c3447faf6140585e622fe78883f2e5fe56f59e8cfa62bbdd208b5ce2f51264",
  "private": false,
  "record": {
    "abstract": "Action of finite-dimensional Hopf algebra $H$ on commutative $k-$algebra $A$\nis considered. As a generalization of the well-known fact for finite groups S.\nMontgomery raised a problem in 1993 whether $A$ is integral over subalgebra of\ninvariants $A^H$. Recently some new results were obtained. Using the properties\nof coradical filtration of pointed Hopf algebras we verified the truth of the\nhypothesis in tree different cases: 1) Hopf algebra $H$ is commutative; 2) char\n$k = p \u003e 0$; 3) $A$ is integral domain. In spite of numerous partial positive\nresults it turned out that hypothesis of S. Montgomery isn\u0027t true in general.\nThe counteraxamples were built for series of pointed Hopf algebras $A_N, N \\ge\n2$.",
    "arxiv_id": "q-alg/9611017",
    "authors": [
      "Vyacheslav Artamonov",
      "Alexander Totok"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Actions of Pointed Hopf Algebras",
    "url": "https://arxiv.org/abs/q-alg/9611017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "256b711f-dcaf-40d7-8d0d-1125595e51a7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}