{
  "id": "hep-th/9607143",
  "version": "v1",
  "published": "1996-07-17T15:04:57.000Z",
  "updated": "1996-07-17T15:04:57.000Z",
  "title": "Hypersymmetry: a Z_3-graded generalization of supersymmetry",
  "authors": [
    "Viktor Abramov",
    "Richard Kerner",
    "Bertrand Le Roy"
  ],
  "journal": "J.Math.Phys. 38 (1997) 1650-1669",
  "doi": "10.1063/1.531821",
  "categories": [
    "hep-th"
  ],
  "abstract": "We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products only. These relations reflect the action of the Z_3-group, which may be either trivial, i.e. abc=bca=cab, generalizing the usual commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\\pi i)/3}. The usual Z_2-graded structures such as Grassmann, Lie and Clifford algebras are generalized to the Z_3-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles are exposed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-07-17T15:04:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalization",
      "hypersymmetry",
      "supersymmetry",
      "clifford algebras",
      "usual commutativity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 420866
    }
  }
}