Local and $2$-local automorphisms of simple generalized Witt algebras
Yang ChenMathematics Postdoctoral Research Center, Hebei Normal University, Shijiazhuang, Heibei, ChinaKaiming ZhaoDepartment of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada; and School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei, ChinaYueqiang ZhaoSchool of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan, China
2021sv
ABI
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. Furthermore, every 2-local or local automorphism of Witt algebras Wn is an automorphism for all nN. But some simple generalized Witt algebras indeed have 2-local (and local) automorphisms that are not automorphisms.
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