{
  "id": "1907.12587",
  "version": "v1",
  "published": "2019-07-29T18:11:02.000Z",
  "updated": "2019-07-29T18:11:02.000Z",
  "title": "On extensions of algebraic groups",
  "authors": [
    "Mathieu Florence",
    "Giancarlo Lucchini Arteche"
  ],
  "comment": "9 pages, comments welcome :)",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be easily generalizable to other contexts. We give a quick application by proving a finiteness result on these sets over a finite field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-29T18:11:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L99",
      "20G15",
      "18D35"
    ],
    "keywords": [
      "algebraic groups",
      "extensions",
      "classic result",
      "finite field",
      "isomorphism classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}