Classifying tilting complexes over preprojective algebras of Dynkin type

By Takuma Aihara, Yuya Mizuno. 2015

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

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