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Nonlinear maps on simple Lie algebras preserving Lie products. (English) Zbl 1262.17004

Summary: Let \(\mathfrak g\) 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 \(\varphi \) on \(\mathfrak g\) 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:

17B20 Simple, semisimple, reductive (super)algebras
17B30 Solvable, nilpotent (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
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