Bounded derived categories and repetitive algebras

Abstract

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra is of finite global dimension. The purpose of this paper is to investigate the relationship between the derived category and the stable category over the repetitive algebra from various points of view for algebras of infinite global dimension. The most satisfactory results are obtained for Gorenstein algebras, especially for selfinjective algebras.