Quark parastatistics and color gauging

If quarks obey Green parastatistics, a gauge theory of color SU(3) is impossible. One can accommodate such a gauge theory of color with tricolored Fermi quarks or with quarks obeying an octonionic mutant of Green parastatistics invented by Günaydin and Gürsey. Underlying parastatistics we find a new algebraic object, the graded mixed triple system, a generalization of the more familiar Lie triple system concept.