Ladders of compactly generated triangulated categories and preprojective algebras

TL;DR

This paper characterizes conditions for ladders in recollements of compactly generated triangulated categories and demonstrates that the derived category of a Dynkin type preprojective algebra has a periodic infinite ladder.

Contribution

It provides a characterization of when recollements admit ladders and applies this to show the derived category of Dynkin type preprojective algebras has a periodic infinite ladder.

Findings

Recollement ladders are characterized by specific conditions.

The derived category of the preprojective algebra of Dynkin type A_n admits a periodic infinite ladder.

One outer term in the ladder is the derived category of a differential graded algebra.

Abstract

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.