Automorphisms of Repetitive Algebras

Let be the repetitive algebra of a finite dimensional algebra B over a field K by the B-bimodule DB = Hom(B, K), and let ν be the Nakayama automorphism of . We determine the positive automorphisms of such that the orbit algebra /( ν) is isomorphic to a splittable extension algebra of B by the B-bimodule (DB)β for an automorphism β of B, and we characterize weakly symmetric algebras and symmetric algebras of the form /( ν) with a positive automorphism of . As an application, we characterize some class of weakly symmetric algebras with non-periodic generalized standard Auslander–Reiten components.