Almost split sequences in the category of complexes of modules

Abstract

Let Λ be an artin algebra. By letting the Nakayama functor act degree-wise, we define a translation τ in the category of complexes of finitely generated Λ-modules, C(mod Λ). Then we investigate the existence of almost split sequences in the category C(mod Λ). As an application of our results, we see that the full subcategory of D(mod Λ) consisting of complexes isomorphic to perfect complexes admits almost split sequences.