The vanishing of self-extensions over n-symmetric algebras of   quasitilted type
  A ring R satisfies the Generalized Auslander-Reiten Condition if any R-module M with no self-extensions in degrees higher than m must have projective dimension at most m. We prove that this condition is satisfied by all n-symmetric algebras of quasitilted type- a broad class of self-injective algebras where every module is periodic under the Nakayama automorphism. 
Maciej Karpicz and Marju Purin
math.RA math.RT