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Nonlinear maps on simple Lie algebras preserving Lie products. (English) Zbl 1262.17004
Summary: 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 ϕ 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.
MSC:
17B20Simple, semisimple, reductive Lie (super)algebras
17B30Solvable, nilpotent Lie (super)algebras
17B40Automorphisms, derivations and other operators on Lie algebras