Monomial arrow removal and the finitistic dimension conjecture
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912510329749504 |
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| author | Erdmann, Karin Giatagantzidis, Odysseas Psaroudakis, Chrysostomos Solberg, Øyvind |
| author_facet | Erdmann, Karin Giatagantzidis, Odysseas Psaroudakis, Chrysostomos Solberg, Øyvind |
| contents | In this paper, we introduce the monomial arrow removal operation for bound quiver algebras, and show that it is a novel reduction technique for determining the finiteness of the finitistic dimension. Our approach first develops a general method within the theory of abelian category cleft extensions. We then demonstrate that the specific conditions of this method are satisfied by the cleft extensions arising from strict monomial arrow removals. This crucial connection is established through the application of non-commutative Gröbner bases in the sense of Green. The theory is illustrated with various concrete examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monomial arrow removal and the finitistic dimension conjecture Erdmann, Karin Giatagantzidis, Odysseas Psaroudakis, Chrysostomos Solberg, Øyvind Representation Theory Rings and Algebras 16E05, 16E10, 16G20, 18E10, 18G20 In this paper, we introduce the monomial arrow removal operation for bound quiver algebras, and show that it is a novel reduction technique for determining the finiteness of the finitistic dimension. Our approach first develops a general method within the theory of abelian category cleft extensions. We then demonstrate that the specific conditions of this method are satisfied by the cleft extensions arising from strict monomial arrow removals. This crucial connection is established through the application of non-commutative Gröbner bases in the sense of Green. The theory is illustrated with various concrete examples. |
| title | Monomial arrow removal and the finitistic dimension conjecture |
| topic | Representation Theory Rings and Algebras 16E05, 16E10, 16G20, 18E10, 18G20 |
| url | https://arxiv.org/abs/2506.23747 |