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| HAL : hal-00624106, version 2 |
| arXiv : 1109.3405 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (15-09-2011) | v2 (23-02-2012) |
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| Torsors, Reductive Group Schemes and Extended Affine Lie Algebras |
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| Philippe Gille 1Arturo Pianzola 2 |
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| (23/02/2012) |
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| We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that we take draws heavily for the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows us to find a bridge between multiloop algebras and the work of J. Tits on reductive groups over complete local fields. |
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| 1 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris |
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| 2 : | University of Alberta, Canada |
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University of Alberta |
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| Domaine | : | Mathématiques/Anneaux et algèbres Mathématiques/Théorie des représentations Mathématiques/Géométrie algébrique |
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| Reductive group scheme – torsor – multiloop algebra – Extended Affine Lie Algebras. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00624106, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00624106 | |
| oai:hal.archives-ouvertes.fr:hal-00624106 | |
| Contributeur : Philippe Gille | |
| Soumis le : Jeudi 23 Février 2012, 15:11:50 | |
| Dernière modification le : Jeudi 23 Février 2012, 21:42:47 | |
