 |
 |
|
|
| Fiche détaillée | Preprint, Working Paper, Document sans référence, etc. |
 |
|
|
| Versions disponibles : | v1 (22-02-2010) | v2 (26-05-2010) | v3 (15-06-2011) |
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| Preprojective algebras and c-sortable words |
|
|
| Claire Amiot1Osamu Iyama2Idun Reiten3Gordana Todorov4 |
|
|
|
| Let $Q$ be an acyclic quiver and $\Lambda$ be the completion of the 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 $\ww$ of $w$. We are specially interested in the case where the word $\ww$ 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. This nice description allows us to construct a triangle equivalence between the 2-Calabi-Yau triangulated category $\underline{\Sub}\Lambda_w$ and the generalized cluster category associated with an Auslander algebra. |
|
|
|
|
|
|
|
|
|
| 1 : | Mathematisches Institut Bonn |
|
|
| 2 : | Nagoya University |
|
|
| 3 : | IMF - Institutt for matematiske fag |
|
|
| 4 : | neu - Departement of Mathematics [Boston] |
|
|
|
|
|
|
|
| preprojective algebra – quiver representation – generalized cluster category – Coxeter group – 2-Calabi-Yau triangulated category – tilting theory – cluster-tilting |
| hal-00458893, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00458893 | |
| oai:hal.archives-ouvertes.fr:hal-00458893 | |
| Contributeur : Claire Amiot | |
| Soumis le : Lundi 15 Mars 2010, 18:51:15 | |
| Dernière modification le : Mercredi 26 Mai 2010, 15:07:02 | |
