The bounded derived categories of an algebra with radical squared zero

2016/10/19 by Bautista, Raymundo, Liu, Shiping · 3 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.06115

Abstract

Let \La be an elementary locally bounded linear category over a field with radical squared zero. We shall show that the bounded derived category D^b(\ModbLa) of finitely supported left \La-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(\rm mod^b\hspace-2pt\La) of finite dimensional left \La-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 \La such that D^b(\rm mod^b\hspace-2.3pt\La) has only finitely many Auslander-Reiten components.

Cited by

• Auslander-Reiten theory via Nakayama duality in abelian categories
• Classification of silted algebras for two quivers of Dynkin type \mathbbD_n
• Covering techniques in higher Auslander-Reiten theory

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