Stratifying systems over hereditary algebras

This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems cannot be complete. For wild hereditary algebras, with more than two vertices, we show that there exists a complete stratifying system whose elements are regular modules. In any other case, we conclude that there are no stratifying system consisting of regular modules.

Recollements induced from tilting modules over tame hereditary algebras

In this paper, we consider the endomorphism algebra of an infinitely generated tilting module of the form

PURITY RELATIVE TO CLASSES OF FINITELY PRESENTED MODULES

We investigate purities determined by classes of finitely presented modules including the correspondence between purities for left and right modules. We show some cases where purities determined by matrices of given sizes are different. Then we consider purities over finite-dimensional algebras, giving a general description of the relative pure-injectives which we make completely explicit in the case of tame hereditary algebras.

THE AUSLANDER–REITEN SEQUENCES ENDING AT GABRIEL–ROITER FACTOR MODULES OVER TAME HEREDITARY ALGEBRAS

Let Λ = kQ be a finite dimensional hereditary algebra over an algebraically closed field k with Q a quiver of Euclidean type [Formula: see text], [Formula: see text], or [Formula: see text]. We study the Auslander–Reiten sequences terminating at Gabriel–Roiter factor modules and show that for almost all but finitely many Gabriel–Roiter factor modules, the Auslander–Reiten sequences have indecomposable middle terms.

Infinite Dimensional Representations of Canonical Algebras

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to themore general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with canonical algebras. The investigation is centered around the generic and the Prüfer modules, and how other modules are determined by these modules.