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| HAL : hal-00458893, version 3 |
| arXiv : 1002.4131 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (22-02-2010) | v2 (26-05-2010) | v3 (15-06-2011) |
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| Preprojective algebras and c-sortable words |
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| Claire Amiot 1Osamu Iyama 2 |
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| (22/02/2010) |
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| Let $Q$ be an acyclic quiver and $\Lambda$ be the complete preprojective algebra of $Q$ over an algebraically closed field $k$. To any element $w$ in the Coxeter group of $Q$, Buan, Iyama, Reiten and Scott have introduced and studied in \cite{Bua2} a finite dimensional algebra $\Lambda_w=\Lambda/I_w$. In this paper we look at filtrations of $\Lambda_w$ associated to any reduced expression $\mathbf{w}$ of $w$. We are especially interested in the case where the word $\mathbf{w}$ is $c$-sortable, where $c$ is a Coxeter element. In this situation, the consecutive quotients of this filtration can be related to tilting $kQ$-modules with finite torsionfree class. |
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| 1 : | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université de Strasbourg |
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| 2 : | Nagoya University |
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Nagoya University |
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| 3 : | Institutt for matematiske fag (IMF) |
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Trondheim University |
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| 4 : | Departement of Mathematics [Boston] (neu) |
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Northeastern University |
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| Domaine | : | Mathématiques/Théorie des représentations |
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| preprojective algebra – quiver representation – generalized cluster category – Coxeter group – 2-Calabi-Yau triangulated category – tilting theory – cluster-tilting |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00458893, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00458893 | |
| oai:hal.archives-ouvertes.fr:hal-00458893 | |
| Contributeur : Claire Amiot | |
| Soumis le : Mercredi 15 Juin 2011, 10:14:38 | |
| Dernière modification le : Mercredi 15 Juin 2011, 10:17:22 | |
