Classification of table algebras with two basis elements whose product is a linear combination of their conjugates
Table Algebras (A,B) with distinct non-real basis elements a,b ∈ B
satisfying
ab=3Dm‾a + n‾b,
m,n ∈ R+,
are studied in this paper.
The two cases where either a is real and b is non-real or a,b are
both reals were completely classified by Z. Arad and H. Blau.
Here we study the remaining case where a and b are non-real.