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arxiv: 1509.07387 · v3 · pith:7HEKE36Qnew · submitted 2015-09-24 · 🧮 math.RT · math.RA

Classifying tilting complexes over preprojective algebras of Dynkin type

Takuma Aihara , Yuya Mizuno This is my paper
classification 🧮 math.RT math.RA
keywords complexestiltingalgebrasdynkinpreprojectivetypealgebrabijection
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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.

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  1. Fishing for complements

    math.RT 2024-02 unverdicted novelty 5.0

    Necessary and sufficient conditions for complements to presilting objects in triangulated categories are established via co-t-structures, plus an equivalence characterizing silting-discrete algebras.