Hypersymmetry: A Z{sub 3}-graded generalization of supersymmetry
- Laboratoire de Gravitation et Cosmologie Relativistes, Universite Pierre et Marie Curie, CNRS URA 769, Tour 22, 4-eme etage, Boite 142 4, Place Jussieu, 75005 Paris (France)
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z{sub 3}-graded structures. In the new algebraic structures we define, all products of two entities are left free, the only constraining relations being imposed on ternary products. These relations reflect the action of the Z{sub 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{sup (2{pi}i)/3}. The usual Z{sub 2}-graded structures such as Grassmann, Lie, and Clifford algebras are generalized to the Z{sub 3}-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed. {copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 467260
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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