The derived category of an algebra with radical square zero

TL;DR

This paper uses Koszul duality and covering theory to describe the derived category of an algebra with radical square zero as an orbit category, revealing the structure of its Auslander--Reiten quiver components.

Contribution

It introduces a novel description of the derived category of such algebras as an orbit category of an infinite quiver's derived category.

Findings

Connected components of the Auslander--Reiten quiver are classified.

The derived category is realized via an orbit category construction.

Abstract

Koszul duality and covering theory are combined to realise the bounded derived category D of an algebra with radical square zero as a certain orbit category of the bounded derived category of finitely presented representations of an associated infinite quiver. As a consequence, the possible shapes of the connected components of the Auslander--Reiten quiver of D are described.