On the Degree in Categories of Complexes of Fixed Size

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


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.


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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