The octonion (Cayley) algebra is studied in a split basis by means of a formalism that brings out its quark structure. The groups SO(8), SO(7), and G2 are represented by octonions as well as by 8 × 8 matrices and the principle of triality is studied in this formalism. Reduction is made through the physically important subgroups SU(3) and SU(2)⊗ SU(2) of G2, the automorphism group of octonions.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics