{
  "id": "1407.8318",
  "version": "v1",
  "published": "2014-07-31T08:51:14.000Z",
  "updated": "2014-07-31T08:51:14.000Z",
  "title": "Conjugacy classes of $n$-tuples in semi-simple Jordan algebras",
  "authors": [
    "Hannah Bergner"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $J$ be a finite-dimensional semi-simple Jordan algebra over an algebraically closed field of characteristic $0$. In this article, the diagonal action of the automorphism group of $J$ on the $n$-fold product $J\\times\\ldots \\times J$ is studied. In particular, it is shown that the orbit through an $n$-tuple $x=(x_1,,\\ldots,x_n)$ is closed if and only if the Jordan subalgebra generated by the elements $x_1,\\ldots, x_n$ is semi-simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-31T08:51:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy classes",
      "finite-dimensional semi-simple jordan algebra",
      "diagonal action",
      "automorphism group",
      "fold product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8318B"
    }
  }
}