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Lyndon words form a basis for Free Lie algebras.

In this direction, I need the reference for the super Lyndon words for free Lie superalgebras.

Given the definition of super Lyndon words, how to associate Lie monomials to get a basis for Free Lie superalgebras?

Kindly share your thoughts.

Thank you.

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An article you probably want to look at is E. S. Chibrikov, "The Right-Normed Basis for a Free Lie Superalgebra and Lyndon–Shirshov Words", Algebra Logika 45 (2006), issue 4, pp. 458--483. This contains information on constructing a right-normed basis for free Lie superalgebras through the theory of Lyndon-Shirshov words.

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  • $\begingroup$ Thank you. Given the definition of super Lyndon words, how to associate Lie monomials to get a basis for Free Lie superalgebras? This is not given in this paper. Please tell where I can find this. Also, please tell why are we taking u is a Lyndon word in X and v^2 where v is a Lyndon word in X_1 ? $\endgroup$ – GA316 Mar 3 at 10:26

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