Applications of Frobenius Algebras to Representation Theory of Schur Algebras Original Research Article

A Schur algebra is a subalgebra of the group algebraRGassociated to a partition ofG, whereGis a finite group andRis a commutative ring. For two classes of Schur algebras we study the relationship between indecomposable modules over the Schur algebra and overRG, but we discuss this problem in a more general context. Further we develop a character theory for Schur algebras; in particular, we express primitive central idempotents in terms of trace functions and we derive orthogonality relations for trace functions. These results are also presented in a more general context, namely for Frobenius algebras over rings. Moreover, we focus on class functions on Schur algebras.