Sous-algebres de Cartan des algebres de Kac-Moody reelles presque deployees
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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, <b>171</b>, 43-96 (1995)]. 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.
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 58(4), 1009-1030, 2006-10-01
The Mathematical Society of Japan