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We propose a modification of standard QCD description of the colour tripletof quarks describing quark fields endowed with colour degree of freedom byintroducing a 12-component colour generalization of Dirac spinor, with built-inZ_3 grading playing an important algebraic role in quark confinement. In"colour Dirac equations" the SU(3) colour symmetry is entangled with theZ_3-graded generalization of Lorentz symmetry, containing three 6-parametersectors related by Z_3 maps. The generalized Lorentz covariance requiressimultaneous presence of 24 colour Dirac multiplets, which lead to thedescription of all internal symmetries of quarks: besides SU(3) \times SU(2)\times U(1), the flavour symmetries and three quark families.

Z_3 - graded colour Dirac equations for quarks, confinement and generalized Lorentz symmetries