Héctor A. Merklen

Indecomposables in derived categories of gentle algebras

We give a description of the indecomposable objects in the derived category of a finite-dimensional gentle algebra.

Module categories with infinite radical square zero are of finite type

It is well known that an artin algebra A is of finite representation type if and only if red(modA)=0. In this note we deepen this result by showing that(rad(modA))2=0 implies that A is of finite representation type.

Indecomposables in Derived Categories of Skewed-Gentle Algebras

Abstract We give a description of the indecomposable objects in the derived category of a finite-dimensional skewed-gentle algebra.

The grothendieck group of the category of modules of finite projective dimension over certain weakly triangular algebras

In this paper we study the category of finitely generated modules of finite projective dimension over a class of weakly triangular algebras, which includes the algebras whose idempotent ideals have finite projective dimension. In particular, we prove that the relations given by the (relative) almost split sequences generate the group of all relations for the Grothendieck group of P <∞(Λ) if and only if P <∞(Λ) is of finite type. A similar statement is known to hold for the category of all finitely generated modules over an artin algebra, and was proven by C.M.Butler and M. Auslander ( [B] and [A]).