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

Abstract

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]. Keywords Simple Lie algebra • Toral subalgebra • Absolute toral rank Communicated by Vyacheslav Futorny.

On simple $15$-dimensional Lie algebras in characteristic $2$

“…It is straightforward to check that in this basis the multiplication table of C L (h) coincides with the multiplication table of the simple 7-dimensional Hamiltonian algebra H (see [GG,§3] or [GGA, §1]) via the identification…”