Constructions of symmetric separable equivalences and their applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915452207235072 |
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| author | Sun, Juxiang Zhao, Guoqiang |
| author_facet | Sun, Juxiang Zhao, Guoqiang |
| contents | Let $Λ$ and $Γ$ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras of modules. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is an invariant under symmetrical separable equivalences. Moreover, we show that a symmetrical separable equivalence preserves the Frobenius-finite type, Auslander-type condition, the (strong) Nakayama conjecture, the Auslander-Gorenstein conjecture and so on. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of symmetric separable equivalences and their applications Sun, Juxiang Zhao, Guoqiang Representation Theory 16G10, 16D20, 16E10, 16E30 Let $Λ$ and $Γ$ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras of modules. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is an invariant under symmetrical separable equivalences. Moreover, we show that a symmetrical separable equivalence preserves the Frobenius-finite type, Auslander-type condition, the (strong) Nakayama conjecture, the Auslander-Gorenstein conjecture and so on. |
| title | Constructions of symmetric separable equivalences and their applications |
| topic | Representation Theory 16G10, 16D20, 16E10, 16E30 |
| url | https://arxiv.org/abs/2508.14401 |