李超三系的实现

Realization of Lie-supertriple System

在李三系与李代数之间的关系已有研究的基础上,通过类似的方法,即由李超三系先做克罗内克积、再做向量空间,定义一个代数体系,并且证明这个代数体系是李超代数.从而得到特征数不为2的域上的任意李超三系与李超代数之间的关系:任意一个李超三系都可由这种方法得到.

The methods based on the relationship between the Lie-triple System and the Lie algebra,we have defined a algebra by making the Kronecker product and vector space of Lie-supertriple System.And we proved the algebra was a Lie Superalgebra.Thus we proved that the relationship between the Lie-supertriple System and the Lie Superalgebra：that every Lie-supertriple System can be obtained in this way.