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.
CITATION STYLE
Bonfiglioli, A., & Fulci, R. (2012). Construction of free lie algebras. In Lecture Notes in Mathematics (Vol. 2034, pp. 459–477). Springer Verlag. https://doi.org/10.1007/978-3-642-22597-0_8
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