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arXiv · 2107.05440

The algebraic and geometric classification of nilpotent right alternative algebras

Nurlan Ismailov·Ivan Kaygorodov·Manat Mustafa
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Abstract

We present algebraic and geometric classifications of the $4$-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only $9$ non-isomorphic nontrivial nilpotent right alternative algebras. The corresponding geometric variety has dimension $13$ and it is determined by the Zariski closure of $4$ rigid algebras and one one-parametric family of algebras.

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Nurlan Ismailov, Ivan Kaygorodov, Manat Mustafa. 2021-07-02. The algebraic and geometric classification of nilpotent right alternative algebras. https://doi.org/10.1007/s10998-021-00386-x

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