Ladders of compactly generated triangulated categories and preprojective   algebras
  In this paper we characterize when a recollement of compactly generated triangulated categories admits a ladder of some height going either upwards or downwards. As an application, we show that the derived category of the preprojective algebra of Dynkin type $\mathbb{A}_n$ admits a periodic infinite ladder, where the one outer term in the recollement is the derived category of a differential graded algebra. 
Nan Gao and Chrysostomos Psaroudakis
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