In this paper, we prove that every invertible $2$-local or local automorphism of a simple generalized Witt algebra over any field of characteristic $0$ is an automorphism. Furthermore, every $2$-local or local automorphism of Witt algebras $W_n$ is an automorphism for all $n \in \mathbb{N}$. But some simple generalized Witt algebras indeed have $2$-local (and local) automorphisms that are not automorphisms.

中文翻译：

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简单广义Witt代数的局部和$ 2 $-局部自同构

在本文中，我们证明了简单广义Witt代数在特征$ 0 $的任何域上的每个可逆的$ 2 $-局部或局部自同构都是自同构的。此外，维特代数$ W_n $的每$ 2 $-局部或局部自同构是\ mathbb {N} $中所有$ n \\的自同构。但是，某些简单的广义Witt代数确实具有$ 2 $-局部（和局部）自同构，而不是自同构。