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.
Classifying tilting complexes over preprojective algebras of Dynkin type
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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.
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2024 1verdicts
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Fishing for complements
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.