{
  "id": "1111.6292",
  "version": "v2",
  "published": "2011-11-27T20:29:18.000Z",
  "updated": "2011-12-26T15:27:46.000Z",
  "title": "On abstract representations of the groups of rational points of algebraic groups and their deformations",
  "authors": [
    "Igor A. Rapinchuk"
  ],
  "comment": "minor corrections, typos fixed",
  "categories": [
    "math.GR",
    "math.AG"
  ],
  "abstract": "In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank $\\geq 2.$ First, we extend our earlier methods to analyze representations of elementary groups over arbitrary associative rings, and as a consequence, prove the conjecture of Borel and Tits on abstract homomorphisms of the groups of rational points of algebraic groups for groups of the form ${\\bf SL}_{n,D}$, where $D$ is a finite-dimensional central division algebra over a field of characteristic zero. Second, we apply our results to study deformations of representations of elementary subgroups of universal Chevalley groups of rank $\\geq 2$ over finitely generated commutative rings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-26T15:27:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G35"
    ],
    "keywords": [
      "abstract representations",
      "rational points",
      "algebraic groups",
      "finite-dimensional central division algebra",
      "elementary subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6292R"
    }
  }
}