Another Characterization of Tilted Algebras

Tilted Special Biserial Algberas

Tilted algebras, that is endomorphism algebras of tilting modules over a hereditary algebra, have been one of the main objects of study in representation theory of algebras since their introduction by Happel and Ringel [9]. As a generalization, Happel, Reiten and Smalø studied endomorphism algebras of tilting objects of a hereditary abelian category which they call quasi-tilted algebras [8]. We...

Tilted String Algebras

Tilted algebras, that is endomorphism algebras of tilting modules over a hereditary algebra, have been one of the main objects of study in representation theory of algebras since their introduction by Happel and Ringel [10]. As a generalization, Happel, Reiten and Smalø studied endomorphism algebras of tilting objects of a hereditary abelian category which they call quasi-tilted algebras [9]. T...

From Iterated Tilted Algebras to Cluster-tilted Algebras

In this paper the relationship between iterated tilted algebras and cluster-tilted algebras and relation-extensions is studied. In the Dynkin case, it is shown that the relationship is very strong and combinatorial.

Tilting Theory and Cluster Algebras

The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these topics. We will also discuss some of the interplay between cluster algebras on one side and cluster categories/cluster-tilted algebras on the other, as well as feedback from the latter theory to clus...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras