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arXiv · 1703.10506

Local and 2-local derivations and automorphisms on simple Leibniz algebras

Shavkat Ayupov·Karimbergen Kudaybergenov·Bakhrom Omirov
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Abstract

The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz algebra are automatically derivations. We show that nilpotent Leibniz algebras as a rule admit local derivations and 2-local derivations which are not derivations. Further we consider automorphisms of simple Leibniz algebras. We prove that every 2-local automorphism on a complex finite-dimensional simple Leibniz algebra is an automorphism and show that nilpotent Leibniz algebras admit 2-local automorphisms which are not automorphisms. A similar problem concerning local automorphism on simple Leibniz algebras is reduced to the case of simple Lie algebras.

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Shavkat Ayupov, Karimbergen Kudaybergenov, Bakhrom Omirov. 2017-09-08. Local and 2-local derivations and automorphisms on simple Leibniz algebras. https://arxiv.org/abs/1703.10506

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