中文摘要：

研究了双曲型Kac-Moody代数的特殊虚根——极小虚根的基本性质及其对应的Dynkin图的特性,给出了四阶双曲型Kac-Moody代数的极小虚根的计算方法,并计算出了所有四阶双曲型Kac-Moody代数的极小虚根.

英文摘要：

The Kac-Moody algebra of hyperbolic type was focused.The basic properties of minimal imaginary roots which are special imaginary roots and the characteristics of the corresponding Dynkin diagram were investigarted.A method to calculate the minimal imaginary roots of Kac-Moody algebra of hyperbolic type of order 4 was presented and a complete list of them was given.