Integral Table Algebras with a Faithful Nonreal Element of Degree 4

Abstract

Throughout this chapter we assume that (A,B) is a standard integral table algebras generated by a non-real element of degree 4 and min(B) ≥ 3. The structure of the algebras from the class A strongly depends on the structure of the multiset \( [b\bar b] \) where b is a non-real faithful element of B of degree 4. A direct verification shows that the following multisets exhibit all possibilities for \( [b\bar b] \) : [14,62],[14,43],[14,34],[14,42,41], [14,41,41,41],[14,81,41],[14,121].