On representation-finite gendo-symmetric algebras with only one non-injective projective module

Motivated by the relation between Schur algebra and group of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang Steffen Koenig [15], [16] addressed some behaviour endomorphism generator over algebra, which they called gendo-symmetric algebra. Continuing this line works, we classify article representation-finite algebras that have precisely one isomorphism class indecomposable non-injective projective module. We also determine their almost ?-stable derived equivalence classes sense Wei Hu Changchang Xi [21]. It turns out representative can be chosen as quotient socle certain