Igusa-Todorov distances
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912526147518464 |
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| author | Zhang, Jinbi Zheng, Junling |
| author_facet | Zhang, Jinbi Zheng, Junling |
| contents | A new homological dimension, called the Igusa-Todorov distance, is introduced to measure how far an Artin algebra is from being an Igusa-Todorov algebra. An upper bound for the dimension is established in terms of the Loewy length, leading to the conclusion that every Artin algebra has a finite Igusa-Todorov distance.Using this dimension, we derive an upper bound for the dimension of the singularity category. Furthermore, we investigate how the Igusa-Todorov distance behaves under various relationships between algebras. Specifically, we demonstrate that stable equivalences preserve the Igusa-Todorov distances for algebras without nodes, prove that it is an invariant under singular equivalence of Morita type with level, and establish bounds for the distances of algebras involved in a recollement of derived module categories. Consequently, the Igusa-Todorov distance is an invariant under derived equivalences of algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Igusa-Todorov distances Zhang, Jinbi Zheng, Junling Representation Theory 16E05, 16G10, 16E10, 18G80 A new homological dimension, called the Igusa-Todorov distance, is introduced to measure how far an Artin algebra is from being an Igusa-Todorov algebra. An upper bound for the dimension is established in terms of the Loewy length, leading to the conclusion that every Artin algebra has a finite Igusa-Todorov distance.Using this dimension, we derive an upper bound for the dimension of the singularity category. Furthermore, we investigate how the Igusa-Todorov distance behaves under various relationships between algebras. Specifically, we demonstrate that stable equivalences preserve the Igusa-Todorov distances for algebras without nodes, prove that it is an invariant under singular equivalence of Morita type with level, and establish bounds for the distances of algebras involved in a recollement of derived module categories. Consequently, the Igusa-Todorov distance is an invariant under derived equivalences of algebras. |
| title | Igusa-Todorov distances |
| topic | Representation Theory 16E05, 16G10, 16E10, 18G80 |
| url | https://arxiv.org/abs/2405.09958 |