Levi and Malcev Theorems for Finite-Dimensional Algebras from the Variety Defined by the Identities x2 =J(x,y, zu) =0

We study the variety of binary Lie algebras defined by the identities x2 =J(x,y,zu) =0,where J(a,b,c) denotes the Jacobian of a,b,c.Building on previous work by Carrillo,Rasskazova,Sabinina and Grishkov,in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.