{
  "id": "2010.07177",
  "version": "v1",
  "published": "2020-10-14T15:47:35.000Z",
  "updated": "2020-10-14T15:47:35.000Z",
  "title": "Centralisers of formal maps",
  "authors": [
    "Anthony G. O'Farrell"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\\G$. We consider the centraliser $C_g$ of an element $g\\in\\G$ which is tangent to the identity of $\\G$. Elements of finite order always have a large centraliser. If $g$ has infinite order our main result is that $C_g$ is uncountable, and in fact contains an uncountable abelian subgroup. This holds regardless of the characteristic of $K$, but the proof is quite different in finite characteristic than in characteritic zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-14T15:47:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E99"
    ],
    "keywords": [
      "formal maps",
      "formal composition form",
      "characteritic zero",
      "finite dimension",
      "integral domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}