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How can we construct a basis for free Lie-algebra of rank $2$ generated by two elements $a$, $b$ through Lazard-elimination?

Jendrik Stelzner
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Nil
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1 Answers1

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For Lazard-Shirshov elimination see the well-known paper Subalgebras of free Lie algebras by A. I. Shirshov. A survey on this topic including the various constructions of (linear) bases for free Lie algebras on $m\ge 2$ generators is given by Bokut:

Gröbner-Shirshov Bases for Lie Algebras: after A. I. Shirshov

See also here for further references. Hall bases coincide with Lazard-bases. More examples are given in Ralph Stöhr's paper:

Bases, Filtrations and module decompositions of free Lie algebras.

For $2$ generators see this example.

Dietrich Burde
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