Abstract
A classical gauge model based on the Lie group SU (3)L⊗ U (1)N with exotic quarks is reformulated within the formalism of nonassociative geometry associated with an L cycle. The N charges of the fermionic particles and the related parameter constraints are algebraic consequences and are uniquely determined. Moreover, the number of scalar particles is dictated by the nonassociativity of the geometry. As a byproduct of this formalism, the Weinberg angle θw, scalar, charged and neutral gauge boson masses, as well as the mixing angles, are derived. Furthermore, various expressions for the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are obtained.
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