Realizing stable categories as derived categories

In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra A such that A(0) has finite global dimension, we construct two types of triangle-equivalences. First we show that there exists a triangle-equivalence between the stable category of Z-graded A-modules and the derived category of a certain algebra Gamma of finite global dimension. Secondly we show that if A has Gorenstein parameter l, then there exists a triangle-equivalence between the stable category of Z/lZ-graded A-modules and a derived-orbit category of Gamma, which is a triangulated hull of the orbit category of the derived category. 2013 Elsevier Inc. All rights reserved.