The algebraic and geometric classification of derived Jordan and bicommutative algebras
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917399513530368 |
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| author | Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22110 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The algebraic and geometric classification of derived Jordan and bicommutative algebras Abdelwahab, Hani Kaygorodov, Ivan Lubkov, Roman Rings and Algebras 17A30 (primary), 17D15, 14L30 (secondary) 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. |
| title | The algebraic and geometric classification of derived Jordan and bicommutative algebras |
| topic | Rings and Algebras 17A30 (primary), 17D15, 14L30 (secondary) |
| url | https://arxiv.org/abs/2601.22110 |