Luise Unger

Finitistic dimension of standardly stratified algebras

We prove that the projectively and the injectively defined finitistic dimensions of a standardly stratified algebra are always finite by giving the optimal bound for these numbers in terms of the number of simple modules.

Schur modules over wild, finite dimensional path algebras with three simple modules

Abstract Let A=k Δ be the path algebra of a finite, connected quiver Δ without oriented cycles over a field k. Let n be the number of vertices of Δ . An A-module Z is called a Schur module if its endomorphism ring is the ground field, and if Ext1A(Z, Z) = 0. If A is representation finite or tame, or if n = 2, then all Schur modules are known. In this article we consider the first non-trivial case, namely we assume that A is wild, and n = 3. We give an algorithm which determines all regular, τ-sincere Schur modules Z up to τ-translates and all tilting modules with direct summand Z.

Reconstruction of Path Algebras from their Posets of Tilting Modules

Let A = kΔ be the path algebra of a finite quiver without orientedcycles. The set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set. We will show here that T A uniquely determines Δ if Δ has no multiple arrows and no isolated vertices.

Auslander generators of iterated tilted algebras

Let A be an iterated tilted algebra. We will construct an Auslander generator M in order to show that the representation dimension of A is three in case A is representation infinite.

Lower bounds for faithful, preinjective modules

AbstractLet

Almost complete tilting modules

k\overrightarrow \Delta

Standardly Stratified Algebras and Tilting

be the path algebra for some representation-infinite quiver