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

中文翻译：

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关于固定大小配合物类别的度数

我们认为 $$\Lambda $$Λ 是一个艺术代数并且 $$n \ge 2$$n≥2。我们研究如何计算 $${{\mathbf {C_n}}(\mathrm{proj}\, \Lambda )}$$Cn( projΛ) 与长度。我们给出了 $${\mathbf {C_n}}(\mathrm{proj}\, \Lambda )$$Cn(projΛ) 中的复合物之间的不可约态射的核和焦核属于此类的条件。对于代数闭域上的有限维遗传代数 H，我们确定不可约态射何时具有有限左（或右）度，并根据某些不可约态射的度数给出一个表征，其中 $${\mathbf { C_n}}(\mathrm{proj} \,H)$$Cn(projH) 是有限类型。