• 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… 

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