On minimal Auslander-Gorenstein algebras and standardly stratified algebras

We give new properties of algebras with finite self-injective dimension coinciding with the dominant dimension d≥2, which are called minimal Auslander-Gorenstein algebras in the recent work of Iyama and Solberg, see [22]. In particular, when those algebras are standardly stratified, we give criteria when the category of (properly) (co)standardly filtered modules has a nice homological description using tools from the theory of dominant dimensions and Gorenstein homological algebra. We give some examples of standardly stratified algebras having dominant dimension equal to the self-injective dimension, including examples having an arbitrary natural number as the self-injective dimension and blocks of finite representation type of Schur algebras.