Classifying tilting complexes over preprojective algebras of Dynkin type

TL;DR

This paper classifies all tilting complexes over preprojective algebras of Dynkin type by establishing a bijection with the braid group, and determines the derived equivalence classes using silting theory.

Contribution

It introduces a classification of tilting complexes via braid groups and develops criteria for silting-discreteness in triangulated categories.

Findings

Classified all tilting complexes over preprojective algebras of Dynkin type.

Established a bijection between tilting complexes and the braid group.

Determined the derived equivalence classes of these algebras.

Abstract

We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the corresponding folded graph. In particular, we determine the derived equivalence class of the algebra. For the results, we develop the theory of silting-discrete triangulated categories and give a criterion of silting-discreteness.