Let A be a representation-finite simply connected algebra, and TAbe an arbitrary tilting
module (in the sense of Happei and Ringel). We show that B= End TA satisfies the …

Tilting theory has been a central research topic in representation theory for a long time. Let Λ
be a hereditary algebra, T0 be a tilting Λ-module, B:= EndΛ (T0), then B is called a tilted …

It is shown that, given any finite dimensional, split basic algebra λ= KΓ I (where Γ is a quiver
and I an admissible ideal in the path algebra KΓ), there is a finite list of affine algebraic …

Based on the first fundamental theorem of classical invariant theory we present a reduction
technique for computing relative invariants for quivers with relations. This is applied to the …

The fundamental paper of Gabriel on representation-finite quivers [14] already contains a
remark due to Tits, which indicates a close connexion between the representation-type of a …

Let A be a finite dimensional associative algebra with an identity over an algebraically
closed field. Assume moreover that A is basic, connected, and that the ordinary quiver of A …

This is a survey article describing some of the ways in which the theory of rational
representations of algebraic groups interacts with the representation theory of finite …

Associated with each finite directed quiver Q is a quasi-hereditary algebra, the so-called
twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi …

We introduce thread quivers as an (infinite) generalization of quivers, and show that every k-
linear (k algebraically closed) hereditary category with Serre duality and enough projectives …

Tilting modules occur in a variety of contexts and we are fortunate to have a unifying
language with which to describe them. This is provided by the language of quasi-hereditary …