New invariants of stable equivalences of algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912642787966976 |
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| author | Xi, Changchang Zhang, Jinbi |
| author_facet | Xi, Changchang Zhang, Jinbi |
| contents | We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $ν$-dominant dimensions induce stable equivalences of their Frobenius parts. As an application of our new methods developed, we verify the Auslander--Reiten conjecture on stable equivalences for two rather different classes of algebras: principal centralizer matrix algebras over arbitrary fields and Frobenius-finite algebras over algebraically closed fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10848 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | New invariants of stable equivalences of algebras Xi, Changchang Zhang, Jinbi Representation Theory Rings and Algebras Primary 16G10, 16E05, 15A27, Secondary 16D60, 18G80, 16L60 We show that stable equivalences between Artin algebras without nodes preserve homological data that provide upper bounds for finitistic dimension, and that stable equivalences between Artin algebras with positive $ν$-dominant dimensions induce stable equivalences of their Frobenius parts. As an application of our new methods developed, we verify the Auslander--Reiten conjecture on stable equivalences for two rather different classes of algebras: principal centralizer matrix algebras over arbitrary fields and Frobenius-finite algebras over algebraically closed fields. |
| title | New invariants of stable equivalences of algebras |
| topic | Representation Theory Rings and Algebras Primary 16G10, 16E05, 15A27, Secondary 16D60, 18G80, 16L60 |
| url | https://arxiv.org/abs/2207.10848 |