# $\tau^2$-stable tilting complexes over weighted projective lines

Authors
Type
Published Article
Publication Date
Dec 22, 2014
Submission Date
Feb 24, 2014
Identifiers
DOI: 10.1016/j.aim.2014.12.018
Source
arXiv
Let $\mathbb{X}$ be a weighted projective line and $\operatorname{coh}\mathbb{X}$ the associated categoy of coherent sheaves. We classify the tilting complexes $T$ in $D^b(\operatorname{coh}\mathbb{X})$ such that $\tau^2 T\cong T$, where $\tau$ is the Auslander-Reiten translation in $D^b(\operatorname{coh}\mathbb{X})$. As an application of this result, we classify the 2-representation-finite algebras which are derived-equivalent to a canonical algebra. This complements Iyama-Oppermann's classification of the iterated tilted 2-representation-finite algebras. By passing to 3-preprojective algebras, we obtain a classification of the selfinjective cluster-tilted algebras of canonical-type. This complements Ringel's classification of the selfinjective cluster-tilted algebras.