{
  "id": "1306.3965",
  "version": "v1",
  "published": "2013-06-17T19:31:52.000Z",
  "updated": "2013-06-17T19:31:52.000Z",
  "title": "On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras",
  "authors": [
    "Leandro Cagliero",
    "Fernando Szechtman"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\\in K$. When is $F[x,y]=F[\\alpha x+\\beta y]$ for some non-zero elements $\\alpha,\\beta\\in F$?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-17T19:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "13C05",
      "12F10",
      "12E20"
    ],
    "keywords": [
      "representation theory",
      "lie algebras",
      "primitive element",
      "applications",
      "finite dimensional uniserial representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3965C"
    }
  }
}