Tilting modules and dominant dimension with respect to injective modules

Abstract

In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalization of results of Crawley-Boevey-Sauter, Nguyen-Reiten-Todorov-Zhu and Pressland-Sauter. Moreover, we give characterizations of almost $n$-Auslander-Gorenstein algebras and almost $n$-Auslander algebras by the existence of tilting modules. As an application, we describe a sufficient condition for almost $1$-Auslander algebras to be strongly quasi-hereditary by comparing such tilting modules and characteristic tilting modules.

arXiv comment25 pages, major changes, to appear in Q. J. Math

References in corpus (7)

• Auslander correspondence
• Dominant dimensions, derived equivalences and tilting modules
• Special tilting modules for algebras with positive dominant dimension
• Tilting modules over Auslander-Gorenstein Algebras
• From Submodule Categories to the Stable Auslander Algebra
• Strongly quasi-hereditary algebras and rejective subcategories
• Happel's functor and homologically well-graded Iwanaga-Gorenstein algebras

Cited by in corpus (2)

• Higher Morita-Tachikawa correspondence
• On split quasi-hereditary covers and Ringel duality