Generalized table algebras
\textit{Y. Kawada} [Proc. Phys.-Math. Soc. Jap., III. Ser. 24, 97-109 (1942)] defined the concept of a \(C\)-algebra to study the common properties of characters and conjugacy classes in finite groups. The concept of a table algebra was defined by \textit{Z. Arad} and \textit{H. I. Blau} [J. Algebra 138, No. 1, 137-185 (1991; Zbl 0790.20015)] and many interesting results about finite groups were obtained in this context. \(C\)-algebras and table algebras are commutative and they are defined over the complex field \(\mathbb{C}\). In [Algebra Colloq. 5, No. 1, 85-97 (1998; Zbl 0948.20003)] the authors of the present paper studied \(C\)-algebras over the complex field without the assumption of the commutativity of the algebra. In the paper under review they define the concept of an algebra, called a generalized table algebra, similar to that of a noncommutative table algebra but letting the ground field be an integral domain. In this paper interesting results concerning generalized table algebras including their representation theory are obtained.
scientific article; zbMATH DE number 1415558
scientific article