# The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

@article{Jumaniyozov2019TheAA, title={The algebraic and geometric classification of nilpotent noncommutative Jordan algebras}, author={Doston Jumaniyozov and Ivan Kaygorodov and A. Kh. Khudoyberdiyev}, journal={arXiv: Rings and Algebras}, year={2019} }

We give algebraic and geometric classifications of complex $4$-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only $18$ non-isomorphic nontrivial nilpotent noncommutative Jordan algebras. The corresponding geometric variety is determined by the Zariski closure of $3$ rigid algebras and $2$ one-parametric families of algebras.

## 18 Citations

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R A ] 1 J un 2 02 0 The algebraic classification of nilpotent CD-algebras 1

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We give an algebraic classification of complex 4-dimensional nilpotent CD-algebras.

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