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ON THE STRUCTURE OF KAC–MOODY ALGEBRAS

TIMOTHÉE MARQUIS
2020 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
Let A be a symmetrisable generalised Cartan matrix, and let g(A) be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of g(A): given two homogeneous elements x, y ∈ 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 g(A).
doi:10.4153/s0008414x20000358 fatcat:j37ujasqtjfznceksoccxpfgvu