中文摘要：

导子是一种特殊的线性变换,对研究李超三系的结构和表示理论有重要作用.通过讨论李超三系及其标准嵌入李超代数的导子及内导子的性质,得到了完备李超三系的分解定理;并得到了完备李超三系的一个判别条件.

英文摘要：

The derivations which are special linear transformations play an important role on the construction and representation theory of Lie supertriple systems.The properties of the derivation and the inner derivation in Lie supertriple systems or its standard imbedding Lie super algebras are considered.The decomposition theorem of complete Lie supertriple systems and a sufficient condition of complete Lie supertriple systems are obtained.