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Groupes algébriques semi-simples en dimension cohomologique ≤2 pp 121–141Cite as

Groupes exceptionnels

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2238))

Abstract

Le point culminant de ce chapitre est l’étude de la conjecture II pour les groupes de type E 7. On produit aussi une liste de résultats partiels pour les groupes de type exceptionnel de type D 4, E 6 et E 8. Rappelons que le cas des groupes de type G 2 et F 4 a été traité au chapitre précédent, voir le Corollaire 6.0.3.

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Notes

  1. 1.

    C’est un petit calcul de racines; noter que le cas où L∕k est un corps est évident puisque on a alors \(\widehat \mu (k)=0\).

  2. 2.

    On remarque aussi que ce k-groupe H est le centralisateur de son centre C(H) = μ 2. En particulier, H (et DM) est une forme intérieure par application de la Proposition 3.1.15.

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  1. Camille Jordan Institute, CNRS, Université Lyon 1, Villeurbanne, France

    Philippe Gille

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  1. Philippe Gille
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Gille, P. (2019). Groupes exceptionnels. In: Groupes algébriques semi-simples en dimension cohomologique ≤2 . Lecture Notes in Mathematics, vol 2238. Springer, Cham. https://doi.org/10.1007/978-3-030-17272-5_8

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