Irreducible morphisms in the bounded derived category |
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Authors: | Raymundo Bautista,Marí a José Souto Salorio |
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Affiliation: | a Instituto de Matemáticas, UNAM, Unidad Morelia, A.P. 61-3, Xangari, C.P. 58089, Morelia, Michoacán, Mexicob Facultade de Informatica, Campus de Elviña, Universidade da Coruña, CP 15071, A Coruña, Espagne |
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Abstract: | We study irreducible morphisms in the bounded derived category of finitely generated modules over an Artin algebra Λ, denoted , by means of the underlying category of complexes showing that, in fact, we can restrict to the study of certain subcategories of finite complexes. We prove that as in the case of modules there are no irreducible morphisms from X to X if X is an indecomposable complex. In case Λ is a selfinjective Artin algebra we show that for every irreducible morphism f in either fj is split monomorphism for all j∈Z or split epimorphism, for all j∈Z. Moreover, we prove that all the non-trivial components of the Auslander-Reiten quiver of are of the form ZA∞. |
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Keywords: | 16G70 18G35 16G10 18E30 |
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