The derived dimensions and representation distances of artin algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912066077458432 |
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| author | Zheng, Junling Zhang, Yingying |
| author_facet | Zheng, Junling Zhang, Yingying |
| contents | There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give methods for constructing $(m,n)$-Igusa-Todorov algebras. As an application, we present for general artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The derived dimensions and representation distances of artin algebras Zheng, Junling Zhang, Yingying Representation Theory Rings and Algebras 18G20, 16E10, 18E10 There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give methods for constructing $(m,n)$-Igusa-Todorov algebras. As an application, we present for general artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras. |
| title | The derived dimensions and representation distances of artin algebras |
| topic | Representation Theory Rings and Algebras 18G20, 16E10, 18E10 |
| url | https://arxiv.org/abs/2406.16011 |