Cofinite Submodule Closed Categories and the Weyl group

Abstract

We consider hereditary Artin algebras over arbitrary fields and prove that there is a natural bijection between the Weyl groups and the sets of full additive cofinite submodule closed subcategories of the module categories. While Oppermann, Reiten and Thomas have shown this for algebraically closed fields and finite fields, we give a different method of proof that holds independently of the field. In particular, we show a relatively simple way to construct all modules that contain a given preinjective module as a submodule.