Automorphisms of repetitive algebras

[摘要] Let (B) over cap be the repetitive algebra of a finite dimensional algebra B over a field K by the B-bimodule DB = Hom(B, K), and let nu be the Nakayama automorphism of (B) over cap. We determine the positive automorphisms phi of (B) over cap such that the orbit algebra (B) over cap/(phi nu) is isomorphic to a splittable extension algebra of B by the B-bimodule (DB)(beta) for an automorphism beta of B, and we characterize weakly symmetric algebras and symmetric algebras of the form (B) over cap/(phi nu) with a positive automorphism phi of (B) over cap. As an application, we characterize some class of weakly symmetric algebras with non-periodic generalized standard Auslander-Reiten components. (C) 2000 Academic Press.

[发布日期] 2000-10-15

[关键词] repetitive algebra;symmetric algebra;Hochschild extension