Classification of Table Algebras with Two Basis Elements Whose Product Is a Linear Combination of Their Conjugates

Abstract

Table Algebras (A,B) with distinct non-real basis elements a, b∈ B satisfying [Formula: see text], (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 real were completely classified by Arad and Blau. Here, we study the remaining case where a and b are non-real.