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| HAL: hal-00624106, version 2 |
| arXiv: 1109.3405 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-09-15) | v2 (2012-02-23) |
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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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| (2012-02-23) |
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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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| Subject | : | Mathematics/Rings and Algebras Mathematics/Representation Theory Mathematics/Algebraic Geometry |
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| Reductive group scheme – torsor – multiloop algebra – Extended Affine Lie Algebras. |
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| hal-00624106, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00624106 | |
| oai:hal.archives-ouvertes.fr:hal-00624106 | |
| From: Philippe Gille | |
| Submitted on: Thursday, 23 February 2012 15:11:50 | |
| Updated on: Thursday, 23 February 2012 21:42:47 | |
