Almost split real forms for hyperbolic Kac-Moody Lie algebras

Hechmi Ben Messaoud (1, 2)

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

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 symmetrizable hyperbolic KacMoody Lie algebras and we establish a complete list of these forms, in terms of their Satake-Tits index, for the strictly hyperbolic ones and for those which are obtained as (hyperbolic) canonical Lorentzian extensions of affine Lie algebras. These forms are of particular interest in theoretical physics because of their connection to supergravity theories.

Mots clés: hyperbolic Kac-Moody algebras; Lorentzian extensions; real forms

Domaines: Algèbres quantiques [math.QA]

Hechmi Ben Messaoud. Almost split real forms for hyperbolic Kac-Moody Lie algebras. Journal of Physics A: Mathematical and Theoretical, 2006, 39, pp.13659-13690. ⟨10.1088/0305-4470/39/44/004⟩. ⟨hal-00020268⟩