查看文章

We show that a properly stratified algebra is Gorenstein if and only if the characteristic tilting module coincides with the characteristic cotilting module. We further show that properly stratified Gorenstein algebras A enjoy strong homological properties such as all Gorenstein projective modules being properly stratified and all endomorphism rings End A (Δ (i)) being Frobenius algebras. We apply our results to the study of properly stratified algebras that are minimal Auslander-Gorenstein algebras in the sense of Iyama-Solberg and calculate under suitable conditions their Ringel duals. This applies in particular to all centraliser algebras of nilpotent matrices.