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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07310 |
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| _version_ | 1866913650913050624 |
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| author | Cao, Peigen |
| author_facet | Cao, Peigen |
| contents | In the $τ$-tilting theory, there exist two classes of foundamental modules: indecomposable $τ$-rigid modules and left finite bricks. In this paper, we prove the indecomposable $τ$-rigid modules and the left finite bricks are uniquely determined by their Newton polytopes spanned by the dimensional vectors of their quotient modules. This is a kind of generalization of Gabriel's result that the indecomposable modules over path algebras of Dynkin quivers are uniquely determined by their dimensional vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modules determined by their Newton polytopes Cao, Peigen Representation Theory Rings and Algebras 16G20 In the $τ$-tilting theory, there exist two classes of foundamental modules: indecomposable $τ$-rigid modules and left finite bricks. In this paper, we prove the indecomposable $τ$-rigid modules and the left finite bricks are uniquely determined by their Newton polytopes spanned by the dimensional vectors of their quotient modules. This is a kind of generalization of Gabriel's result that the indecomposable modules over path algebras of Dynkin quivers are uniquely determined by their dimensional vectors. |
| title | Modules determined by their Newton polytopes |
| topic | Representation Theory Rings and Algebras 16G20 |
| url | https://arxiv.org/abs/2501.07310 |