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arXiv · 1902.09185

Tilting modules and dominant dimension with respect to injective modules

Takahide Adachi·Mayu Tsukamoto
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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.

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Takahide Adachi, Mayu Tsukamoto. 2019-02-25. Tilting modules and dominant dimension with respect to injective modules. https://doi.org/10.1093/qmath/haaa050

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