Abstract
In this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among their isomorphism classes. In particular, we prove that 𝒥2 and 𝒥3 are irreducible and that 𝒥4 is the union of the Zariski closures of the orbits of two rigid Jordan algebras.
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ACKNOWLEDGMENTS
The authors express their gratitude to the referee for correcting several mistakes and pointing out references [Citation5] and [Citation6].
The first author was supported in part by MTM 2006-09152 and CC607-UCM/ESP-2922.
Notes
Communicated by I. Shestakov.