Gorenstein categories and separable equivalences

2025/06/29 by Guoqiang Zhao, Zhao, Guoqiang, Juxiang Sun +1
Mathematics · #16D20 #16E30 #16G10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.23243

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathscrC be an additive subcategory of left Λ-modules, we establish relations of the orthogonal classes of \mathscrC and (co)res \widetilde\mathscrC 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.

Citations

• Representation dimensions linked by Frobenius bimodules with applications to group algebras
• Proper Resolutions and Gorenstein Categories
• The representation dimension of Hecke algebras and symmetric groups
• Gorenstein projective dimension with respect to a semidualizing module

Related

• Gorenstein homological dimensions and Auslander categories
• Thick subcategories and virtually Gorenstein algebras
• Monomorphism categories, cotilting theory, and Gorenstein-projective modules
• Trivial Maximal 1-Orthogonal Subcategories For Auslander's 1-Gorenstein Algebras
• Eventually homological isomorphisms and Gorenstein projective modules