中文摘要：

通过定义环上的李代数及扭同态，找出环上李代数的自同态构造方法，并将其应用到结合代数、张量代数、对称代数和量子包络代数己Uq（sl2）上。

英文摘要：

In this paper, Lie algebras on a ring and twisted homomorphisms of such Lie algebras are de fined. The way of constructing these twisted endomorphisms is found, and applied to tensor algebra, sym metric algebra and quantum enveloping algebra Uq （sl2）.