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.
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Communicated by Wendy Lowen.
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The first and second authors thankfully acknowledge partial support from CONICET and EXA558/14 from Universidad Nacional de Mar del Plata, Argentina. The third author thankfully acknowledge support from Ministerio Español de Economía y Competitividad and FEDER (FF12014-51978-C2-2-R). The first author is a researcher from CONICET.
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Chaio, C., Pratti, I. & Souto Salorio, M.J. On the Degree in Categories of Complexes of Fixed Size. Appl Categor Struct 27, 435–462 (2019). https://doi.org/10.1007/s10485-019-09557-x
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DOI: https://doi.org/10.1007/s10485-019-09557-x