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

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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.