On $n$-hereditary algebras and $n$-slice algebras
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929416748138496 |
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| author | Guo, Jin Yun Hu, Yanping |
| author_facet | Guo, Jin Yun Hu, Yanping |
| contents | In this paper we show that acyclic $n$-slice algebras are exactly acyclic $n$-hereditary algebras whose $(n+1)$-preprojective algebras are $(q+1,n+1)$-Koszul. We also list the equivalent triangulated categories arising from the algebra constructions related to an $n$-slice algebra. We show that higher slice algebras of finite type appear in pairs and they share the Auslander-Reiten quiver for their higher preprojective components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06879 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On $n$-hereditary algebras and $n$-slice algebras Guo, Jin Yun Hu, Yanping Representation Theory Rings and Algebras 16G20 (Primary), 16G70, 16S37(Secondary) In this paper we show that acyclic $n$-slice algebras are exactly acyclic $n$-hereditary algebras whose $(n+1)$-preprojective algebras are $(q+1,n+1)$-Koszul. We also list the equivalent triangulated categories arising from the algebra constructions related to an $n$-slice algebra. We show that higher slice algebras of finite type appear in pairs and they share the Auslander-Reiten quiver for their higher preprojective components. |
| title | On $n$-hereditary algebras and $n$-slice algebras |
| topic | Representation Theory Rings and Algebras 16G20 (Primary), 16G70, 16S37(Secondary) |
| url | https://arxiv.org/abs/2204.06879 |