Geodesic
On the structure of Kac–Moody algebras
Canadian journal of mathematics, Tome 73 (2021) no. 4, pp. 1124-1152

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DOI

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 $\mathfrak {g}(A)$.
DOI : 10.4153/S0008414X20000358
Mots-clés : Kac-Moody algebras, solvable subalgebras, nilpotent subalgebras 
Marquis, Timothée. On the structure of Kac–Moody algebras. Canadian journal of mathematics, Tome 73 (2021) no. 4, pp. 1124-1152. doi: 10.4153/S0008414X20000358
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     title = {On the structure of {Kac{\textendash}Moody} algebras},
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