{
  "id": "1301.0488",
  "version": "v2",
  "published": "2013-01-03T15:56:34.000Z",
  "updated": "2013-05-05T10:15:40.000Z",
  "title": "Wide subalgebras of semisimple Lie algebras",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "14 pages; final version, to appear in \"Algebras & Repr. Theory\"",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Let G be a connected semisimple algebraic group over $k$, with Lie algebra $\\g$. Let $\\h$ be a subalgebra of $\\g$. A simple finite-dimensional $\\g$-module V is said to be $\\h$-indecomposable if it cannot be written as a direct sum of two proper $\\h$-submodules. We say that $\\h$ is wide, if all simple finite-dimensional $\\g$-modules are $\\h$-indecomposable. Some very special examples of indecomposable modules and wide subalgebras appear recently in the literature. In this paper, we describe several large classes of wide subalgebras of $\\g$ and initiate their systematic study. Our approach is based on the study of idempotents in the associative algebra of $\\h$-invariant endomorphisms of V. We also discuss a relationship between wide subalgebras and epimorphic subgroups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-05T10:15:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B70",
      "22E47"
    ],
    "keywords": [
      "semisimple lie algebras",
      "simple finite-dimensional",
      "connected semisimple algebraic group",
      "wide subalgebras appear",
      "epimorphic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0488P"
    }
  }
}