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arXiv · 1810.05562

On the structure of Kac-Moody algebras

Timothée Marquis
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Abstract

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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Timothée Marquis. 2018-10-12. On the structure of Kac-Moody algebras. https://doi.org/10.4153/s0008414x20000358

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