The Extension dimension of syzygy module categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915984758013952 |
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| author | Zheng, Junling Tian, Lulu Shu, Qianyu |
| author_facet | Zheng, Junling Tian, Lulu Shu, Qianyu |
| contents | In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large $i$, the $i$-th syzygy module categories of derived equivalent algebras exhibit identical extension dimensions. Furthermore, we establish that the extension dimension of the $i$-th syzygy module category is an invariant under both stable equivalence and separable equivalence for each nonnegative integer $i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Extension dimension of syzygy module categories Zheng, Junling Tian, Lulu Shu, Qianyu Representation Theory In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large $i$, the $i$-th syzygy module categories of derived equivalent algebras exhibit identical extension dimensions. Furthermore, we establish that the extension dimension of the $i$-th syzygy module category is an invariant under both stable equivalence and separable equivalence for each nonnegative integer $i$. |
| title | The Extension dimension of syzygy module categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2405.02921 |