Integer-quaternion formulation of Lambek's representation of fundamental particles and their interactions

Abstract

Lambek's unified classification of the elementary interaction-quanta of the ``Standard model'' is formulated in terms of the 24 units of the integer-quaternion ring, i.e., the tetrahedral group Q_{24}. An extension of Lambek's scheme to the octahedral group Q_{48} may enable to take all three generations of leptons and quarks into account, as well as to provide a quantitative explanation for flavor-mixing.