Let g be a finite dimensional simple Lie algebra over an algebraically closed field K of characteristic 0. A linear map ϕ : g → g is called a local automorphism if for every x in g there is an automorphism ϕ_x of g such that ϕ(x) = ϕ_x(x). We prove that a linear map ϕ : g → g is local automorphism if and only if it is an automorphism or an anti-automorphism.
Local automorphisms of finite dimensional simple Lie algebras
Costantini, Mauro
2019
Abstract
Let g be a finite dimensional simple Lie algebra over an algebraically closed field K of characteristic 0. A linear map ϕ : g → g is called a local automorphism if for every x in g there is an automorphism ϕ_x of g such that ϕ(x) = ϕ_x(x). We prove that a linear map ϕ : g → g is local automorphism if and only if it is an automorphism or an anti-automorphism.
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