Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras

  title={Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras},
  author={Shen Li and Ren{\'e} Marczinzik and Shunhua Zhang},
  journal={Algebra Colloquium},
In this article we investigate the relations between the Gorenstein projective dimensions of [Formula: see text]-modules and their socles for [Formula: see text]-minimal Auslander–Gorenstein algebras [Formula: see text]. First we give a description of projective-injective [Formula: see text]-modules in terms of their socles. Then we prove that a [Formula: see text]-module [Formula: see text] has Gorenstein projective dimension at most [Formula: see text] if and only if its socle has Gorenstein… 
1 Citation

Dominant Auslander-Gorenstein algebras and Koszul duality

. We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their basic properties. We also

Dominant dimension and tilting modules

We study which algebras have tilting modules that are both generated and cogenerated by projective–injective modules. Crawley–Boevey and Sauter have shown that Auslander algebras have such tilting

Auslander-Gorenstein algebras, standardly stratified algebras and dominant dimensions

We give new properties of algebras with finite Gorenstein dimension coinciding with the dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the recent work of Iyama and

Gorenstein Homological Algebra of Artin Algebras

Gorenstein homological algebra is a kind of relative homological algebra which has been developed to a high level since more than four decades. In this report we review the basic theory of


Abstract We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives.

Characterizing When the Category of Gorenstein Projective Modules is an Abelian Category

We find sufficient and necessary conditions for the category of Gorenstein projective modules of an artin algebra being an abelian category, and give another proof for the Auslander–Solberg

A new characterization of Auslander algebras

Let $\Lambda$ be a finite dimensional Auslander algebra. For a $\Lambda$-module $M$, we prove that the projective dimension of $M$ is at most one if and only if the projective dimension of its socle

Finitistic Auslander algebras

Recently, Chen and Koenig in \cite{CheKoe} and Iyama and Solberg in \cite{IyaSol} independently introduced and characterised algebras with dominant dimension coinciding with the Gorenstein dimension

Auslander-Gorenstein algebras and precluster tilting