On simple Lie algebras of dimension seven over fields of characteristic \(2\) (Q436476)

In this paper the authors deal with simple Lie algebras of dimension 7 and absolute toral rank 3 over an algebraically closed field \(k\) of characteristic 2. They show that all simple Kostrikin-Dzhumadil'daev 7-dimensional Lie algebras over \(k\) are isomorphic to the Hamiltonian algebra \(H((2,1), \omega)\). Furthermore, they determine some features of the 2-closure of the Witt-Zassenhaus algebra \(W(1,3)\) and the Hamiltonian algebra \(H((2,1), \omega)\) (such as their group of 2-automorphisms and their varieties of idempotent and nilpotent elements) and present some Cartan decompositions for these algebras.