整环上二阶线性李代数的自同构

Automorphisms of Two-order Linear Lie Algebas over Domains

设Ｒ是有１的交换环，２是Ｒ的单位．本文决定了Ｒ上李代数ｓｌ２（Ｒ）的理想．进而，若Ｒ是整环，本文决定了ｓｌ２（Ｒ）与ｇｌ２（Ｒ）的自同构形式．

Let R be a commutative ring with 1,2 be a unit of R. In this paper the ideals of the Lie algebra sl2(R) are determined. If R is a domain,the automorphisms of sl2(R) and gl2(R) are determined.