On extensions of free nilpotent Lie algebras of type 2

In this paper, we study the structure of Lie algebras which have free t-nilpotent Lie algebras n2,t of type 2 as nilradical and give a detailed construction for them. We prove that the dimension of any Lie algebra g of this class is dimn2,t+k. If g is solvable, k≤2; otherwise, the Levi subalgebra of g is sl2(K), the split simple 3-dimensional Lie algebra of 2×2 matrices of trace zero, and then k≤4. As an application of the main results we get the classification over algebraically closed fields of Lie algebras with nilradical n2,1, n2,2 and n2,3.