On the structure of Kac–Moody algebras

Marquis, Timothée
(2021) Canadian Journal of Mathematics — Vol. Volume 73, n° Issue 4, p. 1124-1152 (2021)

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Let $A$ be a symmetrisable generalised Cartan matrix, and let $\mathfrak g(A)$ be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak g(A)$: given two homogeneous elements $x,y\in\mathfrak g(A)$, when is their bracket $[x,y]$ a nonzero element? As an application of our results, we give a description of the solvable and nilpotent graded subalgebras of $\mathfrak g(A)$.
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Marquis, T. (2021). On the structure of Kac–Moody algebras. Canadian Journal of Mathematics, Volume 73(Issue 4), 1124-1152. https://doi.org/10.4153/s0008414x20000358 (Original work published 2021)