Unital $3$-dimensional structurable algebras: classification, properties and $\rm{AK}$-construction
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866918370178236416 |
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| author | Abdurasulov, Kobiljon Eraliyeva, Maqpal Kaygorodov, Ivan |
| author_facet | Abdurasulov, Kobiljon Eraliyeva, Maqpal Kaygorodov, Ivan |
| contents | This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras for type $(1, 2).$ For each obtained algebra, we describe the derivation algebra, the automorphism group, the lattice of subalgebras and ideals, and functional identities of degree $2$. Furthermore, we investigate the Allison-Kantor construction for the classified algebras. We determine the structure of the resulting $\mathbb{Z}$-graded Lie algebras, providing their dimensions and Levi decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04391 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unital $3$-dimensional structurable algebras: classification, properties and $\rm{AK}$-construction Abdurasulov, Kobiljon Eraliyeva, Maqpal Kaygorodov, Ivan Rings and Algebras This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras for type $(1, 2).$ For each obtained algebra, we describe the derivation algebra, the automorphism group, the lattice of subalgebras and ideals, and functional identities of degree $2$. Furthermore, we investigate the Allison-Kantor construction for the classified algebras. We determine the structure of the resulting $\mathbb{Z}$-graded Lie algebras, providing their dimensions and Levi decompositions. |
| title | Unital $3$-dimensional structurable algebras: classification, properties and $\rm{AK}$-construction |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2603.04391 |