On non-homogeneous tubes and components of type ZA_{\infty} in the bounded derived category.

CHAIO, GONZALEZ CHAIO Y PRATTI

Algebras and Representation Theory

SPRINGER

Lugar: Berlin; Año: 2021 vol. 24 p. 327 - 356

1386-923X

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 $widetilde{A}_n$ or $widetilde{D}_n$.In case the algebras are discrete, we describe the complexes in the mouth of components of type $mathbb{Z}A_{infty}$ of the Auslander-Reiten quiver of their bounded derived category.