Let X be a weighted projective line and coh X the associated category of coherent sheaves. We classify the tilting complexes T in Db(coh X) such that τ2T ≅ T , where τ is the Auslander–Reiten translation in Db(coh 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.
Subject classification (UKÄ)
- Algebra and Logic