Algebra publication
Title
Applications of Frobenius algebras
to representation theory of Schur algebras
Author(s)
L. Delvaux, E. Nauwelaerts.
Year
1996
Abstract
A Schur algebra is a subalgebra of the group algebra RG associated
to a partition of G,
where G is a finite group and R is a commutative ring.
Schur algebras over the complex numbers
were introduced by Schur and Wielandt, and were first studied by
Tamaschke and Roesler.
For two classes of Schur algebras we study the relationship between
indecomposable modules
over the Schur algebra and over RG, but we discuss this
problem in a more general
context. 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.
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