The algebraic and geometric classification of noncommutative Jordan algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915095316004864 |
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| author | Abdelwahab, Hani Abdurasulov, Kobiljon Kaygorodov, Ivan |
| author_facet | Abdelwahab, Hani Abdurasulov, Kobiljon Kaygorodov, Ivan |
| contents | In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of complex $3$-dimensional noncommutative Jordan algebras. As a byproduct, we obtain the classification of complex $3$-dimensional Kokoris, standard, generic Poisson, and generic Poisson--Jordan algebras; and also complex $4$-dimensional nilpotent Kokoris and standard algebras. In addition, we consider the geometric classification of varieties of cited algebras, that is the description of its irreducible components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic and geometric classification of noncommutative Jordan algebras Abdelwahab, Hani Abdurasulov, Kobiljon Kaygorodov, Ivan Rings and Algebras In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of complex $3$-dimensional noncommutative Jordan algebras. As a byproduct, we obtain the classification of complex $3$-dimensional Kokoris, standard, generic Poisson, and generic Poisson--Jordan algebras; and also complex $4$-dimensional nilpotent Kokoris and standard algebras. In addition, we consider the geometric classification of varieties of cited algebras, that is the description of its irreducible components. |
| title | The algebraic and geometric classification of noncommutative Jordan algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2407.05429 |