Contractions of Low-Dimensional Nilpotent Jordan Algebras

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 2 and 3 are irreducible and that 4 is the union of the Zariski closures of the orbits of two rigid Jordan algebras