How we can write the elements of a free Lie algebra? Is there any reference concerning about this subject? yours,
Francesco.
How we can write the elements of a free Lie algebra? Is there any reference concerning about this subject? yours, Francesco. 


The key words are "Lyndon words". A reference is Free Lie Algebras by C. Reutenauer. 


"Lie Algebras: Theory and Algorithms" by Willem A. De Graaf has a chapter dealing with the more general problem of explicit construction of a basis of a finitely presented Lie algebra (free Lie algebra modulo an ideal), perhaps it is what you are looking for. 

