Sous-algèbres de Cartan des algèbres de Kac-Moody affines réelles presque compactes.Report as inadecuate




Sous-algèbres de Cartan des algèbres de Kac-Moody affines réelles presque compactes. - Download this document for free, or read online. Document in PDF available to download.

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

Abstract : 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.

keyword : Kac-Moody algebra Cartan subalgebra almost compact real form





Author: Hechmi Ben Messaoud - Guy Rousseau -

Source: https://hal.archives-ouvertes.fr/



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