A characterisation of nilpotent Lie algebras by invertible Leibniz-derivations

Details A characterisation of nilpotent Lie algebras by invertible Leibniz-derivations A characterisation of nilpotent Lie algebras by invertible Leibniz-derivations

2010-11-29

arxiv.org/abs/1011.6186v1

Mathematics

Rings and Algebras

Scientific paper

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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