Tilting modules and the subcategories CiM

In this article we further study the full subcategories Ci M of the category of finitely generated modules over an Artin algebra introduced in Platzeck and Pratti (2000), consisting of the modules having an addM resolution of length i, which remains exact under the functor Hom A(M, -). In particular, we characterize tilting modules in terms of these categories and determine when the transpose of a tilting module is a tilting module.Fil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Pratti, Nilda Isabel. Universidad Nacional de Mar del Plata; Argentin

On sectional paths in a category of complexes of fixed size

We show how to build the Auslander-Reiten quiver of the category Cn(proj A)of complexes of size n ≥ 2, for any artin algebra A. We also give conditions over the complexes in Cn(proj A) under which the composition of irreducible morphisms in sectional paths vanishes.Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Pratti, Nilda Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Souto-Salorio, M. José. Universidad de Coruña; Españ

On Non-Homogeneous Tubes and Components of Type ℤA∞ in the Bounded Derived Category

By the knitting technique introduced to build the Auslander-Reiten quiver of the category of complexes of fixed size, it is possible to obtain the Auslander-Reiten triangles in the bounded derived category. To show this technique, we consider two different families of finite dimensional algebras over an algebraically closed field. We describe the complexes that belong to the mouth of non-homogeneous tubes in the Auslander-Reiten quiver of their bounded derived category, whenever this algebras are either derived equivalent to hereditary algebras of type A~ n or D~ n. In case the algebras are discrete, we describe the complexes in the mouth of components of type ℤA∞ of the Auslander-Reiten quiver of their bounded derived category.Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Gonzalez Chaio, Alfredo. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Pratti, Nilda Isabel. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentin

Morphisms in the infinite radical of the bounded derived category

We study necessary conditions for a morphism in the category of complexes of fixed size Cn(proj A), with n \geq 2 and A an artin algebra, to belong to the infinite radical of K^{-,b}(projA).As an application we consider A a Nakayama gentle algebra, whose ordinary quiver is an oriented cycle and we prove that the irreducible morphisms in Cn(proj A) are irreducible in K^{-,b}(projA) or belong to the infinite radical of K^{-,b}(projA). We characterize the irreducible morphisms between indecomposable complexes in Cn(proj A) that belong to the infinite radical of K^{-,b}(projA) for $A$ a Nakayama gentle algebra not selfinjective. For the case of a Nakayama gentle selfinjective algebra, we characterize the irreducible morphisms between indecomposable complexes in Cn(proj A) that belong to the infinite radical of the bounded homotopic category in terms of their left and right degrees.Fil: Chaio, Claudia Alicia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Chaio, Alfredo González. Universidad Nacional de Mar del Plata; ArgentinaFil: Pratti, Nilda Isabel. Universidad Nacional de Mar del Plata; Argentin

On the type of a category of complexes of fixed size and the strong global dimension

We prove that if the strong global dimension η of an algebra A is finite, then Cη+ 1(proj A) is of finite type if and only if for each n ≥ 2, Cn(projA) is of finite type. Moreover, we also prove some implications in order to know if for some positive integer is Cn(projA) of infinite type. We determine the strong global dimension of some piecewise hereditary finite dimensional algebras taking into account their ordinary quivers with relations.Fil: Chaio, Claudia Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Gonzalez Chaio, Alfredo. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Pratti, Nilda Isabel. Universidad Nacional de Mar del Plata; Argentin

On m-cluster tilted algebras and trivial extensions

In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial extension of another iterated tilted algebra which is derived equivalent to the original one. We give a procedure to find this new iterated tilted algebra. These m-cluster tilted algebras are quotients of higher relation extensions.Fil: Fernández, Elsa Adriana. Universidad Nacional de la Patagonia; ArgentinaFil: Pratti, Nilda Isabel. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Trepode, Sonia Elisabet. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin