{
  "id": "2103.13731",
  "version": "v1",
  "published": "2021-03-25T10:20:19.000Z",
  "updated": "2021-03-25T10:20:19.000Z",
  "title": "Gradings allowing wild automorphisms",
  "authors": [
    "Anton Trushin"
  ],
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "In 2004 Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a Z-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that can not be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing graded-wild automorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T10:20:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R10",
      "13A02",
      "13N15",
      "13A50"
    ],
    "keywords": [
      "graded-wild automorphisms",
      "nagata automorphism",
      "polynomial algebra",
      "elementary automorphisms respecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}