Sous-algèbres de Cartan des algèbres de Kac-Moody réelles presque déployées

Hechmi Ben Messaoud (1) , Guy Rousseau (2)

1 Département de Mathématiques [Monastir]
2 IECN - Institut Élie Cartan de Nancy

The classification of almost split real forms of symmetrizable Kac-Moody Lie algebras is a rather straightforward infinite-dimensional generalization of the classification of real semi-simple Lie algebras in terms of the Tits index [J. Algebra 171 (1995), 43-96]. We study here the conjugate classes of their Cartan subalgebras under the adjoint groups or the full automorphism groups. Maximally split Cartan subalgebras of an almost split real Kac-Moody Lie algebra are mutually conjugate and one can generalize the Sugiura classification (given for real semi-simple Lie algebras) by comparing any Cartan subalgebra to a standard maximally split one. As in the classical case, we prove that the number of conjugate classes of Cartan subalgebras is always finite.

Mots clés: Kac-Moody algebra; Cartan subalgebra; almost split; real form

Domaines: Théorie des groupes [math.GR]

Hechmi Ben Messaoud, Guy Rousseau. Sous-algèbres de Cartan des algèbres de Kac-Moody réelles presque déployées. J. Math. Soc. Japan, 2006, 58, pp.1009-1030. ⟨hal-00094860⟩