  The wave equation generalizing the Dirac operator to the Z3-graded case is
introduced, whose diagonalization leads to a sixth-order equation. It
intertwines not only quark and anti-quark state as well as the "u" and "d"
quarks, but also the three colors, and is therefore invariant under the product
group Z2 x Z2 x Z3. The solutions of this equation cannot propagate because
their exponents always contain non-oscillating real damping factor. We show how
certain cubic products can propagate nevertheless. The model suggests the
origin of the color SU(3) symmetry and of the SU(2) x U(1) that arise
automatically in this model, leading to the full bosonic gauge sector of the
Standard Model.
