{
  "id": "1605.09342",
  "version": "v1",
  "published": "2016-05-30T17:52:00.000Z",
  "updated": "2016-05-30T17:52:00.000Z",
  "title": "Cohomology of Lie algebras of polynomial vector fields on the line over field of characteristic $2$",
  "authors": [
    "Felix V. Weinstein"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a field $\\mathbb{F}$, let $L_k(\\mathbb{F})$ be the Lie algebra of derivations $f(t)\\frac{d}{dt}$ of the polynomial ring $\\mathbb{F}[t]$, where $f(t)$ is a polynomial of degree $>k$. For any $k\\>1$, we build a basis of the space of continuous cohomology of the Lie algebra $L_k(\\mathbb{F})$ with coefficients in the trivial module $\\mathbb{F}$ for the case where ${\\rm char}(\\mathbb{F})=2$. The result obtained is similar to the famous Goncharova's Theorem for the case ${\\rm char}(\\mathbb{F})=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-30T17:52:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56"
    ],
    "keywords": [
      "polynomial vector fields",
      "lie algebra",
      "characteristic",
      "trivial module",
      "famous goncharovas theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}