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On the Degree in Categories of Complexes of Fixed Size

  • Claudia Chaio
  • Isabel Pratti
  • María José Souto SalorioEmail author
Article
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Abstract

We consider \(\Lambda \) an artin algebra and \(n \ge 2\). We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander–Reiten component of \({{\mathbf {C_n}}(\mathrm{proj}\, \Lambda )}\) with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in \({\mathbf {C_n}}(\mathrm{proj}\, \Lambda )\) 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 \({\mathbf {C_n}}(\mathrm{proj} \,H)\) is of finite type.

Keywords

Irreducible morphisms Auslander–Reiten quiver Degree Kernel Cokernel 

Mathematics Subject Classification

16G70 18G35 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centro Marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de Mar del PlataMar del PlataArgentina
  2. 2.Facultade de InformaticaUniversidade da CoruñaA CoruñaSpain

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