Lorentz and SU(3) Groups Derived from Cubic Quark Algebra

Abstract

We show how Lorentz and SU(3) groups can be derived from the covariance principle conserving a Z₃-graded three-form on a Z₃-graded cubic algebra representing quarks endowed with non-standard commutation laws. This construction suggests that the geometry of space-time can be considered as a manifestation of symmetries of fundamental matter fields.