Cartan subalgebras of almost split real Kac-Moody Lie algebras. (Sous-algèbres de Cartan des algèbres de Kac-Moody réelles presque déployées.) (French) Zbl 1121.17014

A generalization of real forms of semisimple Lie algebras is given by the corresponding real forms of Kac-Moody algebras. Like happens in the Lie algebra case, for the real base field we can find non-conjugate classes of subalgebras. For Kac-Moody algebras, two types of real forms are given, according to the conjugacy classes of Borel subalgebras: the almost compact and the almost split forms. These two classes have been analyzed in detail by different authors.
In the present work, maximally split Cartan subalgebras of almost split Kac-Moody algebras are studied. Their conjugacy allows to proceed like in the Lie algebra case (the so-called Sugiura classification), that is, comparing Cartan subalgebras to maximally split Cartan subalgebras. Among other structural results, it is proven that the number of conjugacy classes is finite. This article is part of an exhaustive analysis of Cartan subalgebras of Kac-Moody algebras due to the authors.


17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras


Zbl 0823.17034
Full Text: DOI Euclid


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