Ladders of compactly generated triangulated categories and preprojective algebras

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.

v1: This articles replaces arXiv:1605.08114, new section is added, title has changed, 19 pages. v2: few typos fixed, comments are welcome. v3: revised version, title has changed, to appear in Applied Categorical Structures