Auslander-Gorenstein algebras and precluster tilting

We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into n-precluster tilting subcategories and τn-selfinjective algebras, where we show that a subcategory naturally associated to n-precluster tilting subcategories has a higher Auslander-Reiten theory. Furthermore, we give a bijection between n-precluster tilting subcategories and n-minimal Auslander-Gorenstein algebras, which is a higher dimensional analog of Auslander-Solberg correspondence [8] as well as a Gorenstein analog of n-Auslander correspondence [22]. The Auslander-Reiten theory associated to an n-precluster tilting subcategory is used to classify the n-minimal Auslander-Gorenstein algebras into four disjoint classes. Our method is based on relative homological algebra due to Auslander-Solberg.