Morphisms in the infinite radical of the bounded derived category

Abstract

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.