一类不定型Kac-Moody李代数

A New Kind of Indefinite Type Kac-Moody Lie Algebra

本文给出新的一类不定型Kac－Moody李代数──SH型李代数的定义，完全刻划了它的虚根，证明了不可分解SH型Cartan矩阵为“good”，且给出不可分解可对称化的广义Cartan矩阵为SH型李代数的Cartan矩阵的一个充分必要条件。

This paper gives the definition of a new kind of indefinite type Kac-Moody lie algebra that is SH type Kac-Moody lie algebra. The imaginary roots systems were completely described.It is proved that an indecomposable cartan matrix of SH type is good finally. We give a necessary and sufficient condition for SH type cartan matries.