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
DOI: 10.2140/ant.2017.11.1287
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 for silting-discreteness.

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