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

Abstract

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.