Model structures and recollements induced by duality pairs

TL;DR

This paper characterizes Gorenstein projective modules related to duality pairs, constructs associated model structures, and explores their applications to Frobenius pairs and ring descriptions.

Contribution

It provides new characterizations of Gorenstein modules and constructs novel model structures and recollements linked to duality and Frobenius pairs.

Findings

Equivalent characterizations of Gorenstein $(rak{L}, rak{A})$-projective modules.

Construction of model structures associated with duality and Frobenius pairs.

Descriptions of rings via Frobenius pairs.

Abstract

We give some equivalent characterizations of $\mathcal{GP}$, the class of Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules, and construct some model structures associated to duality pairs and Frobenius pairs. Moreover, some rings are described by Frobenius pairs. Meanwhile, we investigate strongly Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and obtain some equivalent characterizations of them. Also, some model structures and recollements associated to strongly Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules are constructed.