Part II - On antisymmetric homogeneous integral table algebras of degree three

This paper determines the homogeneous integral table algebras of degree thr ee in which the given basis has a faithful element and has no nontrivial el ements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group un der the action of a fixed-point-free automorphism of order three.