Vol. 11, No. 6, 2017

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Classifying tilting complexes over preprojective algebras of Dynkin type

Takuma Aihara and Yuya Mizuno

Vol. 11 (2017), No. 6, 1287–1315

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 for silting-discreteness.

preprojective algebras, tilting complexes, silting-discrete, braid groups, derived equivalences
Mathematical Subject Classification 2010
Primary: 16G10
Received: 19 February 2016
Revised: 5 February 2017
Accepted: 17 April 2017
Published: 16 August 2017
Takuma Aihara
Department of Mathematics
Tokyo Gakugei University
Tokyo 184-8501
Yuya Mizuno
Graduate School of Mathematics
Nagoya University
Nagoya 464-8602