Algebres de lie orthogonales et formes trilineaires alternees

Abstract

The study of orthogonal Lie algebras is close to the study of trilinear alternate forms. Here, we show that the classification of 2-stepnilpotent orthogonal Lie algebras reduces to the classification of trilinear alternate forms. In a similar way, simple Lie algebras of dimension 8 help classifying orbits of trilinear forms of rank 8. Results presented here are taken from the first author's doctoral thesis. Some undefined terms can be found in references [6], [7] and [8].