A note on random samples of Lie algebras
  Recently, Paiva and Teixeira (arXiv:1108.4396) showed that the structure constants of a Lie algebra are the solution of a system of linear equations provided a certain subset of the structure constants are given a-priori. Here it is noted that Lie algebras generated in this way are solvable and their derived subalgebras are Abelian if the system of linear equations considered by Paiva and Teixeira is not degenerate. An efficient numerical algorithm for the calculation of their structure constants is described. 
Georg Beyerle
math.RT