On standardly stratified algebras

摘要

Let A be a finite dimensional algebra over an algebraically closed field k. For any fixed partial ordering of an index set, Lambda say, labelling the simple A-modules L(i), there are standard modules, denoted by Delta(i), i E A. By definition, Delta(i) is the largest quotient of the projective cover of L(i) having composition factors L(j) with j less than or equal to i. Denote by F(Delta) the category of A-modules which have a filtration whose quotients are isomorphic to standard modules. The algebra A is said to be standardly stratified if all projective A-modules belong to F(Delta). In this paper we define a "stratifying system" and we show that this produces a module Y, whose endomorphism ring A is standardly stratified. In particular, we construct stratifying systems for special biserial self-injective algebras. References: 9