On properly stratified Gorenstein algebras

[摘要] 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 Aenjoy strong homological properties such as all Gorenstein projective modules being properly stratified and all endomorphism rings End(A)(Delta(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. (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] Properly stratified algebras;Minimal Auslander-Gorenstein algebras;Gorenstein algebras;Tilting modules;Dominant dimension