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Nonlinear Maps on Simple Lie Algebras Preserving Lie Products |
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| Authors: | Dengyin Wang Yanxia Zhao Zhengxin Chen |
| Institution: | 1. Department of Mathematics , China University of Mining and Technology , Xuzhou, China wdengyin@126.com;3. Department of Mathematics , China University of Mining and Technology , Xuzhou, China;4. School of Mathematics and Computer Science , Fujian Normal University , Fuzhou, China |
| Abstract: | Let 𝔤 be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero. It is proved in this article that a bijective map ? on 𝔤 preserves Lie products if and only if it is a composition of a Lie algebra automorphism and a bijective map extended by an automorphism of the base field. |
| Keywords: | Automorphisms of Lie algebras Nonlinear maps Simple Lie algebras |