{
  "id": "1710.05280",
  "version": "v1",
  "published": "2017-10-15T06:16:37.000Z",
  "updated": "2017-10-15T06:16:37.000Z",
  "title": "On the module structure over the Steenrod algebra of the Dickson algebra",
  "authors": [
    "Nguyen Sum"
  ],
  "comment": "10 pages",
  "journal": "Quynhon University Journal of Science, Vol. 1, No. 3 (2007), 5-15",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $p$ be an odd prime number. We study the problem of determining the module structure over the mod $p$ Steenrod algebra $\\mathcal A(p)$ of the Dickson algebra $D_n$ consisting of all modular invariants of general linear group $GL(n,\\mathbb F_p)$. Here $\\mathbb F_p$ denotes the prime field of $p$ elements. In this paper, we give an explicit answer for $n=2$. More precisely, we explicitly compute the action of the Steenrod-Milnor operations $St^{S,R}$ on the generators of $D_n$ for $n=2$ and for either $S=\\emptyset, R=(i)$ or $S=(s), R=(i)$ with $s,i$ arbitrary nonnegative integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-15T06:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S10",
      "55P47",
      "55Q45",
      "55T15"
    ],
    "keywords": [
      "steenrod algebra",
      "dickson algebra",
      "module structure",
      "odd prime number",
      "general linear group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}