{
  "id": "1103.2753",
  "version": "v2",
  "published": "2011-03-14T19:44:06.000Z",
  "updated": "2011-05-17T19:18:04.000Z",
  "title": "Representation theory of super Yang-Mills algebras",
  "authors": [
    "Estanislao Herscovich"
  ],
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study in this article the representation theory of a family of super algebras, called the \\emph{super Yang-Mills algebras}, by exploiting the Kirillov orbit method \\textit{\\`a la Dixmier} for nilpotent super Lie algebras. These super algebras are a generalization of the so-called \\emph{Yang-Mills algebras}, introduced by A. Connes and M. Dubois-Violette in \\cite{CD02}, but in fact they appear as a \"background independent\" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras $\\Cliff_{q}(k) \\otimes A_{p}(k)$, for $p \\geq 3$, or $p = 2$ and $q \\geq 2$, appear as a quotient of all super Yang-Mills algebras, for $n \\geq 3$ and $s \\geq 1$. This provides thus a family of representations of the super Yang-Mills algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-17T19:18:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13N10",
      "16S32",
      "17B35",
      "17B56",
      "70S15",
      "81T13"
    ],
    "keywords": [
      "super yang-mills algebras",
      "representation theory",
      "nilpotent super lie algebras",
      "clifford-weyl super algebras",
      "main result states"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-012-1648-z",
      "journal": "Communications in Mathematical Physics",
      "year": 2013,
      "month": "Jun",
      "volume": 320,
      "number": 3,
      "pages": 783
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.320..783H"
    }
  }
}