Classification and construction of Quasisimple Lie algebras

Raphaël Høegh-Krohn (1) , Bruno Torrésani (1)

1 CPT - Centre de Physique Théorique - UMR 6207

We study a class of (possibly intinite-dimensional) Lie algebras, called the Quasisimple Lie algebras (QSLA's), and generalizing semisimple and affine Kac-Mocady Lie algebras. They arc characterized by the existence of a finite-dimensional Carian subalgebra, a non-degenerate symmetric ad-invariant Killing form, and nilpcbtent rootspaces attached to non-isotropic roots. We are then able to derive a clasrification theorem for the possible irreducible elliptic quasisimple root systems; mon!over, we construct explicit realizations of some of them as (untwisted and twisted) current algebras, generalizing the afine loop algebras.

Domaines: Théorie des groupes [math.GR]

Raphaël Høegh-Krohn, Bruno Torrésani. Classification and construction of Quasisimple Lie algebras. Journal of Functional Analysis, 1990, 89 (1), pp.106-136. ⟨10.1016/0022-1236(90)90006-7⟩. ⟨hal-01304308⟩