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arXiv · 2601.22110

The algebraic and geometric classification of derived Jordan and bicommutative algebras

Hani Abdelwahab·Ivan Kaygorodov·Roman Lubkov
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Abstract

We developed a new proper method for classifying $n$-dimensional derived Jordan algebras, and apply it to the classification of $3$-dimensional derived Jordan algebras. As a byproduct, we have the algebraic classification of $3$-dimensional metabelian commutative algebras and $3$-dimensional derived commutative associative algebras. After that, we introduced a method of classifying $n$-dimensional bicommutative algebras, based on the classification of $n$-dimensional derived commutative associative algebras, and applied it to the classification of $3$-dimensional bicommutative algebras. The second part of the paper is dedicated to the geometric classification of $3$-dimensional metabelian commutative, derived commutative associative, derived Jordan and bicommutative algebras.

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Hani Abdelwahab, Ivan Kaygorodov, Roman Lubkov. 2026-01-29. The algebraic and geometric classification of derived Jordan and bicommutative algebras. https://doi.org/10.1016/j.jpaa.2026.108252

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