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arXiv · 1912.02691

The algebraic and geometric classification of nilpotent noncommutative Jordan algebras

Doston Jumaniyozov·Ivan Kaygorodov·Abror Khudoyberdiyev
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Abstract

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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Doston Jumaniyozov, Ivan Kaygorodov, Abror Khudoyberdiyev. 2019-12-03. The algebraic and geometric classification of nilpotent noncommutative Jordan algebras. https://doi.org/10.1142/s0219498821502029

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