Certain representation algebras

Abstract

Let Λ be the set of inequivalent representations of a finite group over a field . Λ is made the basis of an algebra over the complex numbers , called the representation algebra, in which multiplication corresponds to the tensor product of representations and addition to direct sum. Green [5] has shown that if char (the non-modular case) or if is cyclic, then is semi-simple, i.e. is a direct sum of copies of . Here we consider two modular, non-cyclic cases, viz, where is or 4 (alternating group) and is of characteristic 2.