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arXiv · 2003.13893

Local and $2$-local automorphisms of simple generalized Witt algebras

Yang Chen·Kaiming Zhao·Yueqiang Zhao
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Abstract

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. In particular, 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.

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Yang Chen, Kaiming Zhao, Yueqiang Zhao. 2020-03-31. Local and $2$-local automorphisms of simple generalized Witt algebras. https://arxiv.org/abs/2003.13893

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