Canadian Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-05-20 , DOI: 10.4153/s0008414x20000358 Timothée Marquis
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 $\mathfrak {g}(A)$ .
中文翻译:
关于 Kac-Moody 代数的结构
令A为可对称广义 Cartan 矩阵,并令 $\mathfrak {g}(A)$ 为对应的 Kac-Moody 代数。在本文中,我们解决了以下关于 $\mathfrak {g}(A)$ 结构的基本问题 :给定两个同构元素 $x,y\in \mathfrak {g}(A)$ ,它们的括号 $何时是 [x,y]$ 一个非零元素?作为我们结果的应用,我们描述了 $\mathfrak {g}(A)$ 的可解和幂零分级子代数 。