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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.15802 |
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| _version_ | 1866908555963006976 |
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| author | Luo, Yongle Wei, Jiaqun |
| author_facet | Luo, Yongle Wei, Jiaqun |
| contents | Let $A$ be a basic finite-dimensional algebra and denote by $\operatorname{tors} A$ the collection of all all torsion classes of $A$. It has been proved in \cite{Demonet} that $\operatorname{tors} A$ is always a completely semidistributive lattice. In the present paper, we investigate the distributivity of this lattice and proved that the lattice is distributive if and only if the algebra is the finite direct product of finite-dimensional local algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15802 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distributivity in lattices of torsion classes over finite-dimensional algebras Luo, Yongle Wei, Jiaqun Representation Theory 16S90, 06D99 Let $A$ be a basic finite-dimensional algebra and denote by $\operatorname{tors} A$ the collection of all all torsion classes of $A$. It has been proved in \cite{Demonet} that $\operatorname{tors} A$ is always a completely semidistributive lattice. In the present paper, we investigate the distributivity of this lattice and proved that the lattice is distributive if and only if the algebra is the finite direct product of finite-dimensional local algebras. |
| title | Distributivity in lattices of torsion classes over finite-dimensional algebras |
| topic | Representation Theory 16S90, 06D99 |
| url | https://arxiv.org/abs/2303.15802 |