| Orateur(s) | Steffen OPPERMANN - Trondheim,
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| Titre | Stable categories of $(n+1)$-preprojective algebras |
| Date | 05/06/2009 |
| Horaire | 09:00 à 10:00 |
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| Diffusion | |
| Résume | This is joint work with Osamu Iyama. We call an algebra is $n$-representation finite if it has global dimension at most $n$, and its module category contains an $n$-cluster tilting object. In this talk I will first explain how $n$-representation finite algebras give rise to self-injective $(n+1)$-preprojective algebras (= the endomorphism ring of the algebra in its $n$-Amiot cluster category). For $n=2$ (and under certain vanishing conditions more generally) the converse also holds. Thus we can apply a result of Ringel to obtain a complete classification of iterated tilted $2$-representation finite algebras. The stable module category of these self-injective $(n+1)$-preprojective algebras is $(n+1)$-Calabi-Yau. I will explain how it can be identified with the $(n+1)$-Amiot cluster category of a related algebra. |
| Salle | 175 rue du Chevaleret - 75013 Paris |
| Adresse | |
