SH型广义Cartan矩阵及其虚根

SUPER HYPEROBOLIC TYPE GENERALIZED CARTAN MATRICES AND ITS IMAGINARY ROOTS

本文给出了超双曲型Ｃａｒｔａｎ矩阵的定义并讨论了它的虚根的情况，得出一个漂亮的结果，完全刻划了它的虚根。同时也讨论了不可分好的超双曲Ｃａｒｔａｎ矩阵的分类和奇异性等问题，最后得出不可分解可对称化矩阵为超双曲型的一个充要条件。

This paper gave to definition of super hyperbolic type Kac一Moody Lie algebra and discussed thesystem of its imaginary roots.A good result is obtained. It also discussed the problems of the classification and nonsingularity,Finally it gave a nccessary and sufficient condition.