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Ternary Z6-graded algebras

In: Physical and Mathematical Aspects of Symmetries

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  • Richard Kerner

    (Université Pierre et Marie Curie, LPTMC)

Abstract

We investigate the possibility of combining the usual Grassmann algebras with their ternary Z3-graded counterpart, thus creating a more general algebrawith coexisting quadratic and cubic constitutive relations.We study a particular case of algebras generated by two types of variables, ξa and θA, satisfying quadratic and cubic relations respectively, ξa ξb = –ξb ξa and θAθBθC =j θBθCθA a$$EQUATION$$ θ A θ B θ C = j2 θ B θ C θ A ; with j = e $$EQUATION$$ 2pi 3 . We show how one can combine the Z2 and the Z3 gradings of those binary and ternary algebras and merge them into a common Z6-graded algebra.

Suggested Citation

  • Richard Kerner, 2017. "Ternary Z6-graded algebras," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 195-201, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_29
    DOI: 10.1007/978-3-319-69164-0_29
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