The bounded derived categories of an algebra with radical squared zero

Abstract

Let Λ be an elementary locally bounded linear category over a field with radical squared zero. We shall show that the bounded derived category Db(ModbΛ) of finitely supported left Λ-modules admits a Galois covering which is the bounded derived category of almost finitely co-presented representations of a gradable quiver. Restricting to the bounded derived category Db(modbΛ) of finite dimensional left Λ-modules, we shall be able to describe its indecomposable objects, obtain a complete description of the shapes of its Auslander–Reiten components, and classify those Λ such that Db(modbΛ) has only finitely many Auslander–Reiten components.