On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908433714774016 |
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| author | Chust, Viktor Coelho, Flávio U. |
| author_facet | Chust, Viktor Coelho, Flávio U. |
| contents | In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann's well-behaved functors, which compare the mesh category with the module category, and discuss how the properties of these functors can be applied to study the problem of composing irreducible morphisms, which is the problem of deciding when the composition of n irreducible morphisms is non-zero and lies on the (n+1)-th power of the radical. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_03121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms Chust, Viktor Coelho, Flávio U. Representation Theory Primary 16G70, Secondary 16G20, 16B50 In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann's well-behaved functors, which compare the mesh category with the module category, and discuss how the properties of these functors can be applied to study the problem of composing irreducible morphisms, which is the problem of deciding when the composition of n irreducible morphisms is non-zero and lies on the (n+1)-th power of the radical. |
| title | On Riedtmann's well-behaved functors and applications to composites of irreducible morphisms |
| topic | Representation Theory Primary 16G70, Secondary 16G20, 16B50 |
| url | https://arxiv.org/abs/2507.03121 |