{
  "id": "1609.08304",
  "version": "v1",
  "published": "2016-09-27T08:14:29.000Z",
  "updated": "2016-09-27T08:14:29.000Z",
  "title": "An order theoretic characterization of spin factors",
  "authors": [
    "Bas Lemmens",
    "Mark Roelands",
    "Hent van Imhoff"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "The famous Koecher-Vinberg theorem characterizes the Euclidean Jordan algebras among the finite dimensional order unit spaces as the ones that have a symmetric cone. Recently Walsh gave an alternative characterization of the Euclidean Jordan algebras. He showed that the Euclidean Jordan algebras correspond to the finite dimensional order unit spaces $(V,C,u)$ for which there exists a bijective map $g\\colon C^\\circ\\to C^\\circ$ with the property that $g$ is antihomogeneous, i.e., $g(\\lambda x) =\\lambda^{-1}g(x)$ for all $\\lambda>0$ and $x\\in C^\\circ$, and $g$ is an order-antimorphism, i.e., $x\\leq_C y$ if and only if $g(y)\\leq_C g(x)$. In this paper we make a first step towards extending this order theoretic characterization to infinite dimensional JB-algebras. We show that if $(V,C,u)$ is a complete order unit space with a strictly convex cone and $\\dim V\\geq 3$, then there exists a bijective antihomogeneous order-antimorphism $g\\colon C^\\circ\\to C^\\circ$ if and only if $(V,C,u)$ is a spin factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-27T08:14:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17C65",
      "46B40"
    ],
    "keywords": [
      "order theoretic characterization",
      "spin factor",
      "finite dimensional order unit spaces",
      "euclidean jordan algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}