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arXiv · 1803.03142

Local automorphisms on finite-dimensional Lie and Leibniz algebras

Shavkat Ayupov·Karimbergen Kudaybergenov
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Abstract

We prove that a linear mapping on the algebra \(\mathfrak{sl}_n\) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an anti-automorphism. We also show that a linear mapping on a simple Leibniz algebra of the form \(\mathfrak{sl}_n\dot +\mathcal{I}\) is a local automorphism if and only if it is an automorphism. We give examples of finite-dimensional nilpotent Lie algebras \(\mathcal{L}\) with \(\dim \mathcal{L} \geq 3\) which admit local automorphisms which are not automorphisms.

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Shavkat Ayupov, Karimbergen Kudaybergenov. 2018-03-07. Local automorphisms on finite-dimensional Lie and Leibniz algebras. https://arxiv.org/abs/1803.03142

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