• Corpus ID: 126045351

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

@article{Messaoud2006SousalgbresDC,
  title={Sous-alg{\`e}bres de Cartan des alg{\`e}bres de Kac-Moody affines r{\'e}elles presque compactes.},
  author={Hechmi Ben Messaoud and Guy Rousseau},
  journal={Journal of Lie Theory},
  year={2006},
  volume={17},
  pages={1-25}
}
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… 
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Background Citations
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5 Citations

Sous-algèbres de Cartan des algèbres de Kac-Moody réelles presque déployées
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…
Pseudo-symmetric pairs for Kac-Moody algebras
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable KacMoody algebras.…
Almost split real forms for hyperbolic
A Borel-Tits theory was developped for almost split forms of symmetrizable Kac-Moody Lie algebras [J. of Algebra 171, 43-96 (1995)]. In this paper, we look to almost split real forms for…
Almost split real forms for hyperbolic Kac-Moody Lie algebras
A Borel–Tits theory was developed for almost split forms of symmetrizable Kac–Moody Lie algebras. In this paper, we look to almost split real forms and their restricted root systems for symmetrizable…
Vogan diagrams of twisted affine Kac–Moody Lie algebras
A Vogan diagram is a Dynkin diagram of a Kac-Moody Lie algebra of finite or affine type overlayed with additional structures. This paper develops the theory of Vogan diagrams for almost compact real…

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