Type: Article

Irreducible morphisms in the bounded derived category

Raymundo Bautista; María José Souto Salorio;

Abstract:

We study irreducible morphisms in the bounded derived category of finitely generated modules over an Artin algebra A. denoted D(b) (Lambda mod), by means of the underlying category of complexes showing that, in fact, we can restrict to the study of certain subcategories of finite complexes. We prove that as in the case of modules there are no irreducible morphisms from X to X if X is an indecomposable complex. In case Lambda is a selfinjective Artin algebra we show that for every irreducible morphism f in C(b) (Lambda proj) either f(j) is split monomorphism for all j is an element of Z or split epimorphism, for all j is an element of Z. Moreover, we prove that all the non-trivial components of the Auslander-Reiten quiver of C(b)(Lambda proj) are of the form ZA(infinity). (C) 2010 Elsevier B.V. All rights reserved.