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arXiv · 1506.00732

A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

Ivan Kaygorodov·Yury Popov
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Abstract

Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (-1,1)-, quasiassociative, quasialternative, right alternative and Malcev-admissible noncommutative Jordan algebras over the field of characteristic zero. Also, we describe all Leibniz-derivations of semisimple Jordan, right alternative and Malcev algebras.

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Ivan Kaygorodov, Yury Popov. 2015-06-02. A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations. https://doi.org/10.1016/j.jalgebra.2016.02.016

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