Hypersymmetry: a Z_3-graded generalization of supersymmetry

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.

References in corpus (3)

• On Foundation of the Generalized Nambu Mechanics
• Z_3-graded exterior differential calculus and gauge theories of higher order
• A Z_3-graded generalization of supermatrices

Cited by in corpus (35)

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• Approximate Homomorphisms of Ternary Semigroups
• Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
• Exterior differentials of higher order and their covariant generalization
• Fractional Super Lie Algebras and Groups
• Ternary generalization of Pauli's principle and the Z6-graded algebras
• n=3 Nilpotent differential calculus on some non-commutative (super) spaces
• Non-Abelian Fractional Supersymmetry in Two Dimensions
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• Spacetime Symmetries and Z_3-graded Quark Algebra
• The partially alternating ternary sum in an associative dialgebra
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• Notes on Cohomologies of Ternary Algebras of Associative Type
• A Clifford Algebra Approach to Chiral Symmetry Breaking and Fermion Mass Hierarchies
• Geometry of Majorana neutrino and new symmetries
• Generalized Grassmann algebras and applications to stochastic processes
• On the tensor product construction for q-differential algebras
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• Covariant q-Differential Calculus and its Deformations at q^N=1
• Extensions of hom-Lie color algebras
• Universal imbedding of a Hom-Lie Triple System
• On the construction of generalized Grassmann representatives of state vectors
• Stability of homomorphisms and derivations in $C^{\ast }$-ternary algebras
• Hyperpolyadic structures
• Polyadic systems, representations and quantum groups
• Stability of the Jensen--type functional equation in ternary Banach algebras: An alternative fixed point approach
• Hypersymmetry field rotation angle
• A first approach to the Galois group of chaotic chains
• Enveloping algebras of color hom-Lie algebras
• Jordan derivations on $C^{\ast }$-ternary algebras for a Cauchy-Jensen functional equation
• $Z_3$-graded analogues of Clifford algebras and generalization of supersymmetry