Classifying tilting complexes over preprojective algebras of Dynkin type

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.

arXiv comment23 pages

References in corpus (9)

• Cluster structures for 2-Calabi-Yau categories and unipotent groups
• Silting mutation in triangulated categories
• Kac-Moody groups and cluster algebras
• Rigid modules over preprojective algebras
• Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes
• Topological aspects of completely integrable foliations
• Introduction to $\tau$-tilting theory
• Derived autoequivalences from periodic algebras
• Quotient closed subcategories of quiver representations

Cited by in corpus (9)

• Classification of two-term tilting complexes over Brauer graph algebras
• Silting objects
• Discreteness of silting objects and t-structures in triangulated categories
• Lattice structure of Weyl groups via representation theory of preprojective algebras
• On the Finiteness of the Derived Equivalence Classes of some Stable Endomorphism Rings
• Report on the finiteness of silting objects
• Tame block algebras of Hecke algebras of classical type
• On $\tau$-tilting finiteness of symmetric algebras of polynomial growth
• Fishing for complements