{
  "id": "0806.4152",
  "version": "v2",
  "published": "2008-06-25T17:00:02.000Z",
  "updated": "2008-07-07T19:19:53.000Z",
  "title": "Dimension of automorphisms with fixed degree for polynomial algebras",
  "authors": [
    "Vesselin Drensky",
    "Jie-Tai Yu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let $K[x,y]$ be the polynomial algebra in two variables over an algebraically closed field $K$. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms $(f,g)$ of $K[x,y]$ such that $\\max\\{\\text{deg}(f),\\text{deg}(g)\\}=n\\geq 2$ is constructible with dimension $n+6$. The same result holds for the automorphisms of the free associative algebra $K< x,y>$. We have also obtained analogues for free algebras with two generators in Nielsen -- Schreier varieties of algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-07T19:19:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13B25",
      "16S10",
      "17A50"
    ],
    "keywords": [
      "polynomial algebra",
      "fixed degree",
      "automorphisms",
      "schreier varieties",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.4152D"
    }
  }
}