Extended Z(3)-graded Lorentz symmetry and quark chromodynamics

We propose a modification of standard QCD description of the color triplet of quarks by introducing a 12-component color generalization of Dirac spinor, with built-in Z(3) grading playing an important algebraic role in quark confinement. In the "color Dirac equations" the SU(3) color symmetry is entangled with the Z(3)-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z3-graded maps. The generalized Lorentz covariance requires simultaneous presence of 12 color Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides SU(3) x SU(2) x U(1), the flavor symmetries and three quark families. We also discuss the generalized gauge fields and show how the Standard Model content appears naturally due to the overall Z(3) x Z(2) x Z(2) symmetry.