The derived category of an algebra with radical square zero

ABSTRACT

Koszul duality and covering theory are combined to realize 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.

KEYWORDS:

• Algebra with radical square zero
• derived category
• Koszul duality
• orbit category
• quiver representation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16E35
• 16E45
• 18E30

Acknowledgment

The author acknowledges support by the National Natural Science Foundation of China No. 11401297 and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. He thanks a referee for very helpful remarks.