Abstract
THE aim of this chapter is twofold. On the one hand (Sect. 8.1), we complete the missing proof from Chap. 2 concerning the existence of a free Lie algebra Lie(X) related to a set X. This proof relies on the direct construction of Lie(X) as a quotient of the free non-associative algebra Lib(X). Furthermore, we prove that Lie(X) is isomorphic to L(K_X_), and the latter provides a free Lie algebra over X.
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© 2012 Springer-Verlag Berlin Heidelberg
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Bonfiglioli, A., Fulci, R. (2012). Construction of Free Lie Algebras. In: Topics in Noncommutative Algebra. Lecture Notes in Mathematics(), vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22597-0_8
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DOI: https://doi.org/10.1007/978-3-642-22597-0_8
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22596-3
Online ISBN: 978-3-642-22597-0
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