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, k2 otherwise, the Levi subalgebra of g is sl2(K), the split simple 3-dimensional Lie algebra of 2;times&2 matrices of trace zero, and then k4. 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. © 2014 Published by Elsevier Inc