{
  "id": "2004.03095",
  "version": "v1",
  "published": "2020-04-07T02:58:12.000Z",
  "updated": "2020-04-07T02:58:12.000Z",
  "title": "Iwasawa Decomposition for Lie Superalgebras",
  "authors": [
    "Alexander Sherman"
  ],
  "comment": "18 pages; comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $\\theta$ an involution of $\\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $\\theta$ or $\\delta\\circ\\theta$ admits an Iwasawa decomposition, where $\\delta$ is the canonical grading automorphism $\\delta(x)=(-1)^{\\overline{x}}x$. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra $\\mathfrak{g}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-07T02:58:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iwasawa decomposition",
      "basic simple lie superalgebra",
      "nondegenerate invariant form",
      "semisimple automorphisms",
      "general result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}