2-local automorphisms on finite-dimensional Lie algebras

2016/02/16 by Ayupov, Shavkat, Kudaybergenov, Karimbergen · 3 citations
#17A36 #17B20 #17B40 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1602.05187

Abstract

We prove that every 2-local automorphism on a finite-dimensional semi-simple Lie algebra L over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie algebra L with dim L≥ 2 admits a 2-local automorphism which is not an automorphism.

Cited by

• Local and 2-Local automorphisms of n-dimensional totally graded filiform Lie algebras
• Local, 2-local derivations and biderivations on 3-parameter generalized quaternion
• Local superderivation and super-biderivation on generalized quaternion algebra

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• Local automorphisms of finite dimensional simple Lie algebras
• Local automorphisms on finite-dimensional Lie and Leibniz algebras
• Local derivations and automorphisms of nilpotent Lie algebra
• Biderivations, local and 2-local derivation and automorphism of simple ω-Lie algebras
• Local derivations on finite-dimensional Lie algebras