Symmetry of Endomorphism Algebras

Abstract

Motivated by recent problems regarding the symmetry of Hecke algebras, we investigate the symmetry of the endomorphism algebra E P (M) for P a p-group and M a kP -module with k a field of characteristic p. We provide a complete analysis for cyclic p-groups and the dihedral 2-groups. For the dihedral 2-groups, this requires the classification of the indecomposable modules in terms of string modules and band modules. We generalize our techniques to consider E Λ (M) for Λ a Nakayama algebra, a local algebra, or even an arbitrary algebra.