Homological theory of representations having pure acyclic injective resolutions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915176129757184 |
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| author | Yang, Gang Li, Qihui Wang, Junpeng |
| author_facet | Yang, Gang Li, Qihui Wang, Junpeng |
| contents | Let $Q$ be a quiver and $R$ an associative ring. A representation by $R$-modules of $Q$ is called strongly fp-injective if it admits a pure acyclic injective resolution in the category of representations. It is shown that such representations possess many nice properties. We characterize strongly fp-injective representations under some mild assumptions, which is closely related to strongly fp-injective $R$-modules. Subsequently, we use such representations to define relative Gorenstein injective representations, called Gorenstein strongly fp-injective representations, and give an explicit characterization of the Gorenstein strongly fp-injective representations of right rooted quivers. As an application, a model structure in the category of representations is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological theory of representations having pure acyclic injective resolutions Yang, Gang Li, Qihui Wang, Junpeng K-Theory and Homology 16G20, 18A40, 18G05, 18G20 Let $Q$ be a quiver and $R$ an associative ring. A representation by $R$-modules of $Q$ is called strongly fp-injective if it admits a pure acyclic injective resolution in the category of representations. It is shown that such representations possess many nice properties. We characterize strongly fp-injective representations under some mild assumptions, which is closely related to strongly fp-injective $R$-modules. Subsequently, we use such representations to define relative Gorenstein injective representations, called Gorenstein strongly fp-injective representations, and give an explicit characterization of the Gorenstein strongly fp-injective representations of right rooted quivers. As an application, a model structure in the category of representations is given. |
| title | Homological theory of representations having pure acyclic injective resolutions |
| topic | K-Theory and Homology 16G20, 18A40, 18G05, 18G20 |
| url | https://arxiv.org/abs/2407.21660 |