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

Francesco.

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2 Answers 2

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

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by Christophe Reutenauer, rather –  F. C. Jul 14 '12 at 8:57
    
Thanks for the correction –  Bruce Westbury Jul 14 '12 at 13:46

"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.

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