Type: Article

Tame and wild theorem for the category of modules filtered by standard modules

Bautista, R.; Pérez, E.; Salmerón, L.;

Abstract:

We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove a tame-wild dichotomy for the category of ?-filtered modules for an arbitrary finite homological system . This includes the case of standardly stratified algebras. Moreover, in the tame case, we show that given a fixed dimension d, for every d-dimensional indecomposable module , with the only possible exception of those lying in a finite number of isomorphism classes, the module M coincides with its Auslander-Reiten translate in . Our proofs rely on the equivalence of with the module category of some special type of ditalgebra.