Abstract. We
investigate certain Z3-graded
associative algebras with cubic Z3-invariant constitutive relations. 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(
The relationship of this construction with the
operators defining quark states is also considered, and a third-order analogue
of the Klein-Gordon equation is introduced. Cubic products of its solutions may
provide the basis for the familiar wave functions satisfying Dirac and Klein-Gordon equations.