In this paper, we study, for an artin algebra, the class L A (and R A ) which is a full subcategory of the category mod A of finitely generated A-modules, and which consists of all indecomposable A-modules whose predecessors (and successors) have projective dimension (and injective dimension, respectively) at most one. We consider quotient algebras of A, which contain the information on these classes, then define and characterize those algebras for which the class is L A is contravariantly finite (and R A is covariantly finite, respectively).While defining the class of quasi-tilted algebras in [17], Happel, Reiten, and Smalø have introduced two classes of modules which turned out to be very useful in the representation theory of algebras. Let A be an artin algebra, and mod A denote the category of finitely generated right A-modules, then the class L A (or R A ) is the full subcategory

We prove that the representation dimension of a tilted, or of a strict laura algebra, is at most three.

Let H be a hereditary abelian k-category with tilting object and D b (H) denote the bounded derived category of H. This paper is devoted to a study of suspended subcategories of D b (H) by means of their Ext-projectives.The concept of a t-structure in a triangulated category T was introduced in the early eighties in [10]. It was meant as a technique for constructing various abelian subcategories of T ("hearts" of the t-structures) and is helpful for understanding the structure of T . Our motivation for their study comes from the representation theory of Artin algebras, which involves the derived category as an essential tool. There, t-structures are useful due to their relationship with tilting theory (see, for instance, [12,17]). In [17], Keller and Vossieck exhibited a bijection between t-structures in a given triangulated category T and contravariantly finite suspended subcategories of T , called aisles.Our objective in this paper is to study t-structures and aisles, from the point of view of the Ext-projectives. The concept of Ext-projective in a subcategory of a module category was introduced by Auslander and Smalø in their study of relative almost split sequences [7]. Since then, they were useful in various contexts (see [1,4,11]). In our situation, it follows from [17,11] that the Ext-projectives in an aisle U are the projectives in the heart of the t-structure determined by U. Moreover, if U is generated by the Ext-projectives, then the heart of the t-structure is a module category. This explains our interest in them.

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.