Sous-algèbres de Cartan des algèbres de Kac-Moody affines réelles presque compactes.
Résumé
Almost compact real forms of affine Kac-Moody Lie algebras have been already classified [J. Algebra 267, 443-513]. In the present paper, we study the conjugate classes of their Cartan subalgebras under the adjoint groups or the full automorphism groups. Maximally compact Cartan subalgebras are all conjugated to a standard one $h$ and one may compare any Cartan subalgebra to $h$. Cartan subalgebras are related to non compact unitary roots of $h$ and one can see especially that the number of the conjugate classes is always finite. This approach is a generalization of the classification by J. Carmona of Cartan subalgebras for real semi-simple Lie algebras which is different from (but equivalent to) that of Sugiura. The approach of Sugiura which consists in comparing any Cartan subalgebra to a maximally split one does not adapt to our framework of study, as maximally split Cartan subalgebras are not conjugated in general.
Domaines
Théorie des groupes [math.GR]
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_04b2_Sous-algebres_de_Cartan_des_algebres_de_Kac-Moody_affines_reelles_presque_compactes_H.BenMessaoud-G.R_.pdf (265.67 Ko)
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