Abstract
A class of \(Z_3\)-graded associative algebras with cubic \(Z_3\)-invariantconstitutive relations is investigated. The invariant forms on finite algebras of this type are given in the low dimensional cases with two or three generators. We show how the Lorentz symmetry represented by the \(SL(2, \mathbf{C})\) group emerges naturally without any notion of Minkowskian metric, just as the invariance group of the \(Z_3\)-graded cubic algebra and its constitutive relations. Its representation is found in terms of Pauli matrices. The relationship of this construction with the operators defining quark states is also considered.
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Kerner, R. (2014). Invariance and Symmetries of Cubic and Ternary Algebras. In: Makhlouf, A., Paal, E., Silvestrov, S., Stolin, A. (eds) Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55361-5_37
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DOI: https://doi.org/10.1007/978-3-642-55361-5_37
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