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| Detailed view | Preprint, Working Paper, ... |
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| Available versions: | v1 (2010-02-22) | v2 (2010-05-26) | v3 (2011-06-15) |
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| Preprojective algebras and c-sortable words |
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| Claire Amiot1Osamu Iyama2Idun Reiten3Gordana Todorov4 |
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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: | IRMA - Institut de Recherche Mathématique Avancée |
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| 2: | Nagoya University |
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| 3: | IMF - Institutt for matematiske fag |
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| 4: | neu - Departement of Mathematics [Boston] |
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| preprojective algebra – quiver representation – generalized cluster category – Coxeter group – 2-Calabi-Yau triangulated category – tilting theory – cluster-tilting |
| hal-00458893, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00458893 | |
| oai:hal.archives-ouvertes.fr:hal-00458893 | |
| From: Claire Amiot | |
| Submitted on: Wednesday, 15 June 2011 10:14:38 | |
| Updated on: Wednesday, 15 June 2011 10:17:22 | |
