On the periodicity of the Auslander-Reiten translation and the Nakayama functor for the enveloping algebra of self-injective Nakayama algebras

Abstract

In this paper, we describe the structures of the left Be-modules τBei(B) and NBei(B) for i⩾0, where B is a certain finite dimensional selfinjective Nakayama algebra, Be is the enveloping algebra of B, τBe is the Auslander-Reiten translation in the category mod (Be) of finitely generated left Be-modules and NBe:mod(Be)→mod(Be) is the Nakayama functor. Moreover, we compute the τBe-period and the NBe-period of B.