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arXiv · 2407.21660

Homological theory of representations having pure acyclic injective resolutions

Gang Yang·Qihui Li·Junpeng Wang
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Abstract

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.

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Gang Yang, Qihui Li, Junpeng Wang. 2024-07-31. Homological theory of representations having pure acyclic injective resolutions. https://doi.org/10.1007/s00025-025-02368-8

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