On the structure of Kac-Moody algebras

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 $\mathfrak{g}(A)$.

32 pages. Final version, to appear in Canadian Journal of Mathematics

References in corpus (1)

• Eisenstein series and automorphic representations