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. 
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  • Journal of Algebra and Computation,
  • 2019
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