特征为0的域上Witt型李代数的自同构群(英文)

Automorphisms of Witt type Lie Algebras in Characteristic 0

研究了一类Witt型李代数自同构群和其相关的交换结合代数的自同构群 ,得到如下结果 :设F为一个特征为0的域 ,t1 ,t=- 2 ,… ,tn 为F上几个交换的变元 ,F(t1 ,t2 ,…tn)表示t1 ,t2 ,… ,tn 生成的分式域 ,令D = ni=1 F ti,则得到一类witt单李代数且有Aut(F(t1 ,t2 ,… ,tn)D) Aut(F(t1 ,t2 ,… ,tn) ) .

In this paper,the group of automorphisms of a class of Witt type Lie algebras and the group of automorphisms of the corresponding commutative associative algebras are realted.As a consequence,the following result is proved.Let F be a field of characteristic 0, t -1,t -2,…,t -n be n commuting variables over F,F(t -1,t -2,…,t -n) be the field of all rational functions.Let D=n i=1 F  t -i .We have the simple Witt type Lie algebra F(t -1,t -2,…,t -n)D. Then Aut (F(t -1,t -2,…,t -n)D)Aut(F(t -1,t -2,…,t -n)).