具有非退化亦型的Z-阶化李超代数

Z GRADED LIE SUPERALGEBRAS WITH A NONSINGULAR TRACE FORM

本文给出了Ｚ－阶化有限维单李超代数具有非退化亦型的一个必要条件．应用这一结果，我们可以得到Ｃａｒｔａｎ 型李超代数Ｘ（ｎ）与Ｘ（ｍ ，ｎ，ｔ）的Ｋｉｌｌｉｎｇ 型是退化的．

Let L is a finite dimensional simple Z graded Lie superalgebra. In this paper, we obtain the necessary conditions that L possesses a nondegenerate trace form. Using this result, we obtain that the Killing forms of Lie superalgebras X(n) and X(m,n,t) of Cartan type are degenerate.