Z-3 graded generalization of Dirac's equation and modified color dynamics

We propose a generalization od Dirac's equation including the discrete Z3 symmetry in order to incorporate the colour variable along with spin and charge, both representing Z2-symmetries. The resulting discrete symmetry group is Z3 x Z2 x Z2, and the corresponding wave functions have 12 components. The corresponding Dirac operator is a 12 x 12 matrix, and diagonalizes only at sixth power, leading to a sixth-order dispersion relations for energy-momentum. The Lorentz invariance is recovered via introduction of extra mutiplets, i.e. flavours and families. The gauge fields reproduce the usual Standard Model, and confinement is obtained via algebraical exclusion principle.