On the classification of simple Lie algebras of dimension seven over fields of characteristic 2

This paper is the second part of paper (Grishkov and Guerreiro in São Paulo J Math Sci v4(1):93–107, 2010 ) about simple 7-dimensional Lie algebras over an algebraically closed field k of characteristic two. In this paper we prove that all simple 7-dimensional Lie algebras over k of absolute toral rank three are isomorphic to the Cartan algebra W 1 or the Hamilton algebra H 2 . We hope to prove that those algebras are the unique simple 7-dimensional Lie algebras over the field k . Observe that in the case of absolute toral rank 2 this fact was proved in [ 2 ].