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arXiv · 1311.3258

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

Elizabeth Jurisich
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Abstract

It is shown that any generalized Kac-Moody Lie algebra g that has no mutually orthogonal imaginary simple roots can be written as the vector space direct sum of a Kac-Moody subalgebra and subalgebras isomorphic to free Lie algebras over certain modules for the Kac-Moody subalgebra. Also included is a detailed discussion of Borcherds' construction of the Monster Lie algebra from a vertex algebra and an elementary proof of Borcherds' theorem relating Lie algebras with `an almost positive definite bilinear form' to generalized Kac-Moody algebras. (Preprint version 1996)

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Elizabeth Jurisich. 2013-11-13. Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra. https://arxiv.org/abs/1311.3258

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