Let A be a symmetrizable generalized Cartan matrix, g(A) thecorresponding Kac-Moody algebra, then a subalgebra h of g(A) is a split Cartan subalgebra if and only if there is a regular locally finite element x such that h=g 0(adx).

• 设A为一可对称化广义Cartan矩阵 ；g(A)为对应的Kac_Moody代数 ；则 g(A)的子代数h为可裂Cartan子代数的充分必要条件为存在正则局部有限元x ；使得h =g0 (adx) .