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Corpus ID: 102493752

Algebras with ternary law of composition combining Z_2 and Z_3 gradings

@article{Abramov2015AlgebrasWT,
title={Algebras with ternary law of composition combining Z\_2 and Z\_3 gradings},
author={Viktor Abramov and Richard Kerner and Olga Liivapuu},
journal={arXiv: Rings and Algebras},
year={2015}
}

In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with coexisting quadratic and cubic constitutive relations.
We recall the classification of ternary and cubic algebras according to the symmetry properties of ternary products under the action of the S_3 permutation group. Instead of only two kinds of binary algebras, symmetric or antisymmetric, here we get four… Expand

We discuss cubic and ternary algebras which are a direct generalization of Grassmann and Cli ord algebras, but with Z3-grading replacing the usual Z2-grading. Elementary properties and structures of… Expand

The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as… Expand

We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above… Expand