Gorenstein categories and separable equivalences

TL;DR

This paper explores how certain categories and modules in algebra are preserved under separable equivalences, providing new insights into Gorenstein categories and tilting modules.

Contribution

It establishes relations of orthogonal classes under separable equivalences and shows preservation of Gorenstein categories and Wakamatsu tilting modules.

Findings

Gorenstein categories are preserved under separable equivalences

Wakamatsu tilting modules are invariant under separable equivalences

Conditions for invariance of G_{C}-projective modules and Auslander classes

Abstract

Let $\mathscr{C}$ be an additive subcategory of left $\Lambda$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_{C}$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences.