On the Degree in Categories of Complexes of Fixed Size

摘要

We consider Lambda an artin algebra and n >= 2. We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander-Reiten component of Cn(proj Lambda) with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in Cn(proj Lambda) belong to such a category. For a finite dimensional hereditary algebra H over an algebraically closed field, we determine when an irreducible morphism has finite left (or right) degree and we give a characterization, depending on the degrees of certain irreducible morphisms, under which Cn(projH)is of finite type.