Local automorphisms of finite dimensional simple Lie algebras

2018/05/29 by Costantini, Mauro · 2 citations
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1805.11338

Abstract

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

Cited by

• Local and 2-Local automorphisms of n-dimensional totally graded filiform Lie algebras
• The relationship between local derivations and local automorphisms of some associative algebras

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