The octonion (Cayley) algebra is studied in a split basis by means of a formalism that brings outs 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.

Topics
Functions and mappings, Quarks
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© 1973 The American Institute of Physics.
1973
The American Institute of Physics
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