Contractions of low-dimensional nilpotent Jordan algebras

Details Contractions of low-dimensional nilpotent Jordan algebras Contractions of low-dimensional nilpotent Jordan algebras

2008-05-25

arxiv.org/abs/0805.3758v1

Mathematics

Rings and Algebras

12 pages, 3 figures

Scientific paper

In this paper 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 them. In particular, we prove that J2 and J3 are irreducible
and that J4 is the union of the Zariski closures of two rigid Jordan algebras.

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