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Hypersymmetry: a Z_3-graded generalization of supersymmetry

Viktor Abramov·Richard Kerner·Bertrand Le Roy
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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^{(2πi)/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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Viktor Abramov, Richard Kerner, Bertrand Le Roy. 1996-07-17. Hypersymmetry: a Z_3-graded generalization of supersymmetry. https://doi.org/10.1063/1.531821

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