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It is shown that any generalized Kac-Moody Lie algebra g that has no mutuallyorthogonal imaginary simple roots can be written as the vector space direct sumof a Kac-Moody subalgebra and subalgebras isomorphic to free Lie algebras overcertain modules for the Kac-Moody subalgebra. Also included is a detaileddiscussion of Borcherds' construction of the Monster Lie algebra from a vertexalgebra and an elementary proof of Borcherds' theorem relating Lie algebraswith `an almost positive definite bilinear form' to generalized Kac-Moodyalgebras. (Preprint version 1996)

Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra