The species and idempotents of the Green algebra of a finite group with a cyclic Sylow subgroup

Abstract

We study the Green algebra A ( k G ) generated by the isomorphism classes of indecomposable kG-modules, where k is a field with char k = p > 0 and G a finite group with a cyclic Sylow p-subgroup. More precisely, we discuss the homomorphisms A ( k G ) → C (called species) and state a formula for the idempotents of A ( k G ) .