A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

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.

References in corpus (2)

• n-ary algebras: a review with applications
• Generalized derivations of (color) n-ary algebras

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