On duality preservability of Auslander-Reiten quivers of derived categories and cluster categories

Abstract

We give sufficient conditions and necessary conditions on duality preservability of Auslander-Reiten quivers of derived categories and cluster categories over hereditary algebras. Meantime, we characterize the condition of generalized path algebras as cleft extensions of path algebras.

Keywords

Dual quiver / Auslander-Reiten quiver / derived category / cluster category

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Higher Education Press and Springer-Verlag Berlin Heidelberg