Enlargements of complexes of fixed size
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911156444069888 |
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| author | Chaio, Claudia Chaio, Alfredo Gonzalez Suarez, Pamela |
| author_facet | Chaio, Claudia Chaio, Alfredo Gonzalez Suarez, Pamela |
| contents | Let $A$ be an artin algebra. The aim of this work is to describe the enlargements of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$, and to study the irreducible morphisms between them. Precisely, we prove that any indecomposable complex in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ or in $\mathbf{C}_{n+1}(\mbox{proj} \,A)$ for $n$ a positive integer is a shift or an enlargement of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$. We also describe the entrances of the irreducible morphisms in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ between enlargements of an indecomposable complex $X$ in $\mathbf{C}_{n}(\mbox{proj} \,A)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enlargements of complexes of fixed size Chaio, Claudia Chaio, Alfredo Gonzalez Suarez, Pamela Representation Theory 16G70, 16G20, 16E10 Let $A$ be an artin algebra. The aim of this work is to describe the enlargements of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$, and to study the irreducible morphisms between them. Precisely, we prove that any indecomposable complex in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ or in $\mathbf{C}_{n+1}(\mbox{proj} \,A)$ for $n$ a positive integer is a shift or an enlargement of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$. We also describe the entrances of the irreducible morphisms in $\mathbf{C}_{[0,n]}(\mbox{proj} \,A)$ between enlargements of an indecomposable complex $X$ in $\mathbf{C}_{n}(\mbox{proj} \,A)$. |
| title | Enlargements of complexes of fixed size |
| topic | Representation Theory 16G70, 16G20, 16E10 |
| url | https://arxiv.org/abs/2509.12374 |