Derivations in 3-Jordan algebras

Abstract

In this paper, we study Lie algebras of derivations of a commutative algebra verifying the identity (x³y)x - x³(xy) = 0, known as the 3-Jordan algebra. We characterize the derivations via a quintuplet description, prove that the ideal J defined in the paper "A Variety containing Jordan and pseudo-composition algebras" is characteristic. We also furnish a necessary and sufficient condition for the ideal M defined in the aforementioned paper to be d-invariant for a derivation d and classify all 3-dimensional dimensionally nilpotent 3-Jordan algebras.