Type: Article

The bounded derived categories of an algebra with radical squared zero

Bustista, Raymundo; Liu, Shiping;

Abstract:

Let A be an elementary locally bounded linear category over a field with radical squared zero. We shall show that the bounded derived category D-b(Mod(b) Lambda) of finitely supported left Lambda-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 D-b(mod(b)Lambda) of finite dimensional left Lambda-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 A such that D-b(mod(b)Lambda) has only finitely many Auslander Reiten components