Free Nilpotent Lie Algebras Admitting Ad-Invariant Metrics
  In this work we find necessary and sufficient conditions for a free nilpotent or a free metabelian nilpotent Lie algebra to be endowed with an ad-invariant metric. For such nilpotent Lie algebras admitting an ad-invariant metric the corresponding automorphisms groups are studied. 
Gabriela Ovando and Viviana del Barco
math.RA