Morfismos en el radical infinito de la categoria derivada Acotada

CHAIO, CLAUDIA , ALFREDO GONZALEZ CHAIO, ISABEL PRATTI.

Virtual

Conferencia; ARTA; 2021

We study necessary conditions for a morphism in the category of complexes of fixed size C_n(proj A), with n \geq 2 and A an artin algebra, to belong to the infinite radical of K^{-,b}(proj A).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 C_n(proj A) are irreducible in K^{-,b}(proj A) or belong to the infinite radical of K^{-,b}(proj A). We characterize the irreducible morphisms between indecomposable complexes in C_n(proj A) that belong to the infinite radical of K^{-,b}(proj A) 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 C_n(proj A) that belong to the infinite radical of the bounded homotopic category in terms of their left and right degrees.