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December 20, 2014

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Kaiming Zhao

Automorphisms of Witt type Lie algebras in characteristic 0, J. Capital Normal University, 24(2003) 1, 5-9.

Aut$F(t_1, t_2,..., t_n)Dsimeq$Aut(F(t_1, t_2,..., t_n)).$
Kaiming Zhao

published: 2003 | Research publication | paper

In this paper, the group of automorphisms of a class of Witt type Lie algebras and the group of automorphisms of the corresponding commutative algebras are related. As a consequence, the following result is proved. Let $F$ be a field of characteristic 0 and $t_1, t_2,..., t_n$ be commuting variables over $F$, $F(t_1, t_2,..., t_n)$ be the field of all rational functions. Let $D=oplus_{i+1}^n Ffrac{partial}{partial t_i}$. We have the simple Witt type Lie algebra $F(t_1, t_2,..., t_n)D$. Then Aut$F(t_1, t_2,..., t_n)Dsimeq$Aut(F(t_1, t_2,..., t_n))$.

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revised May 3/13

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