$Z_3$-graded analogues of Clifford algebras and generalization of supersymmetry

Details $Z_3$-graded analogues of Clifford algebras and generalization of supersymmetry $Z_3$-graded analogues of Clifford algebras and generalization of supersymmetry

1996-07-31

arxiv.org/abs/hep-th/9607241v1

Physics

High Energy Physics

High Energy Physics - Theory

Lecture given at XXI Colloquium on Group Theoretical Methods in Physics, Goslar, 1996. TeX file, no figures, 12 pages

Scientific paper

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 $Z_3$-graded generalization of the simplest algebra of supersymmetries.

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