Hypersymmetry: a Z_3-graded generalization of supersymmetry

Details Hypersymmetry: a Z_3-graded generalization of supersymmetry Hypersymmetry: a Z_3-graded generalization of supersymmetry

1996-07-17

arxiv.org/abs/hep-th/9607143v1

J.Math.Phys. 38 (1997) 1650-1669

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1063/1.531821

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.

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