On the degree in categories of complexes of fixed size
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929499568865280 |
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| author | Chaio, Claudia Pratti, Isabel Souto, Maria Jose |
| author_facet | Chaio, Claudia Pratti, Isabel Souto, Maria Jose |
| contents | We consider $Λ$ an artin algebra and $n \geq 2$. We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander-Reiten component of ${\mathbf{C_n}({\rm proj}\, Λ)}$ with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in $\mathbf{C_n}({\rm proj}\, Λ)$ 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 $\mathbf{C_n}({\rm proj} \,H)$ is of finite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the degree in categories of complexes of fixed size Chaio, Claudia Pratti, Isabel Souto, Maria Jose Representation Theory We consider $Λ$ an artin algebra and $n \geq 2$. We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander-Reiten component of ${\mathbf{C_n}({\rm proj}\, Λ)}$ with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in $\mathbf{C_n}({\rm proj}\, Λ)$ 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 $\mathbf{C_n}({\rm proj} \,H)$ is of finite type. |
| title | On the degree in categories of complexes of fixed size |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2409.08758 |