Wedge-direct sums of group algebras of finite groups

Abstract

The wedge-direct sum of a sequence of semisimple algebras (over an arbitrary field) was introduced in [Xu, B. (2019). Wedge-direct sums of table algebras and applications to association schemes, I. Commun. Algebra 47(8):3309–3328]. The group algebras (over the complex field) of finite groups are a special class of semisimple algebras. In [Xu, B. (2020). Wedge-direct sums of table algebras and applications to association schemes, II. J. Pure Appl. Algebra 224(11):106402], the wedge-direct sum of a sequence of group algebras of finite p-groups is used to obtain the characterization and classification of a class of p-table algebras. In this article, we continue the research in above mentioned articles and characterize, in terms of table algebras, the wedge-direct sum of a sequence of group algebras of arbitrary finite groups. Applications to association schemes will also be discussed.