Blocks of Endomorphism Algebras

Abstract

Let O G be a p-modular group algebra, let H be a subgroup of G containing the normaliser of a p-subgroup P, let A be an O G-module, and B an O H-module. After defining defect groups of blocks of End O G ( A) and of End O H ( B), we associate a certain block of End( O H)( A ↓ H ) with each block of End O G ( A) having defect group P. Similarly, we associate a certain block of End O G ( B ↑ G ) with each block of End O H ( B) with defect group P. These associations are compatible with the correspondences of Brauer and of Green, and, in particular, they partly generalise Brauer′s First and Second Main Theorems. The theory simplifies when working within blocks of group algebras with abelian defect groups.