2-Local automorphisms of finite-dimensional simple Lie algebras

• Published in: Linear algebra and its applications Vol. 486; pp. 335 - 344
• Main Authors: Chen, Zhengxin, Wang, Dengyin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2015
• Subjects: 2-Local automorphisms; Automorphisms; Finite-dimensional simple Lie algebras; 16W25; 17B40; 2-Local automorphisms; Automorphisms; 17B20; Finite-dimensional simple Lie algebras
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2015.08.025

Let F be an algebraically closed field of characteristic 0, L be a finite-dimensional simple Lie algebra of type Al (l≥1), Dl (l≥4), Ek (k=6,7,8) over F. A not necessarily linear map φ:L→L is called a 2-local automorphism if for every x,y∈L there is an automorphism φx,y:L→L, depending on x and y, such that φ(x)=φx,y(x), φ(y)=φx,y(y). In this paper, we prove that any 2-local automorphism of L is an automorphism.