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arXiv · 1011.6186

A characterisation of nilpotent Lie algebras by invertible Leibniz-derivations

Wolfgang Alexander Moens
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Abstract

Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. The proofs are elementary in nature and are based on well-known techniques.

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Wolfgang Alexander Moens. 2010-11-29. A characterisation of nilpotent Lie algebras by invertible Leibniz-derivations. https://arxiv.org/abs/1011.6186

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