Leaps in the depth of compositions of irreducible morphisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912475759247360 |
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| author | Chust, Viktor Coelho, Flávio U. |
| author_facet | Chust, Viktor Coelho, Flávio U. |
| contents | In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the $(n+m+3)$-th power of the radical, but not in the $(n + m + 4)$-th power. Such an algebra may be also supposed to be string and representation-finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Leaps in the depth of compositions of irreducible morphisms Chust, Viktor Coelho, Flávio U. Representation Theory Primary 16G70, Secondary 16G20 In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the $(n+m+3)$-th power of the radical, but not in the $(n + m + 4)$-th power. Such an algebra may be also supposed to be string and representation-finite. |
| title | Leaps in the depth of compositions of irreducible morphisms |
| topic | Representation Theory Primary 16G70, Secondary 16G20 |
| url | https://arxiv.org/abs/2507.08094 |