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Représentations des formes d'une algèbre de Kac-Moody

Abstract : The subject of this thesis is the study of the representations of K-forms of a KacMoody algebra g over K, where K is a field of characteristic 0 and Kits algebraic closure, i.e., the representations of Lie algebras over K, which tensorised by K, become isomorphic to g. There are two classes of these forms : the almost-split and the almost-anisotropic ones. The representations are supposed to be (over K) in the category 0 and we define and study categories Op.t (over K) and Op.t (over K), called parabolic, which seem to be the good context for the representations of almost-split forms. In particular, we show the existen,ce for the categories Op.t[exponentK] of the concept of local composition series and our main result is the classification of the irreductible modules of these categories.
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Submitted on : Thursday, March 29, 2018 - 10:41:50 AM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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  • HAL Id : tel-01746646, version 1



Cécile Barlet-Mathieu. Représentations des formes d'une algèbre de Kac-Moody. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2002. Français. ⟨NNT : 2002NAN10015⟩. ⟨tel-01746646⟩



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