Z3-graded analogues of Clifford algebras and generalization of supersymmetry
نویسنده
چکیده
We define and study the ternary analogues of Clifford algebras. It is proved that the ternary Clifford algebra with N generators is isomorphic to the subalgebra of the elements of grade zero of the ternary Clifford algebra with N+1 generators. In the case N = 3 the ternary commutator of cubic matrices induced by the ternary commutator of the elements of grade zero is derived. We apply the ternary Clifford algebra with one generator to construct the generalization of the simplest algebra of supersymmetries.
منابع مشابه
Hypersymmetry: a Z3-graded generalization of Supersymmetry, J.Math.Phys
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z3-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 Z3-group, which may be either trivial, i.e. abc = bca = cab, generalizing the usual commutativity, or non-tri...
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