The algebraic and geometric classification of noncommutative Jordan superalgebras
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911449789497344 |
|---|---|
| author | Abdelwahab, Hani Kaygorodov, Ivan Khudoyberdiyev, Abror |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Khudoyberdiyev, Abror |
| contents | The algebraic and geometric classifications of complex $3$-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of $3$-dimensional Kokoris and standard superalgebras, and, due to one-to-one correspondences between suitable superalgebras, we have classifications for generic Poisson-Jordan and generic Poisson superalgebras. As a byproduct, we have the algebraic and geometric classification of the variety of $3$-dimensional anticommutative superalgebras and its principal subvarieties: Lie, Malcev, binary Lie, Tortkara, anticommutative $\mathfrak{CD}$-, $\mathfrak{s}_4$-, anticommutative terminal superalgebras, anticommutative conservative and anticommutative quasi-conservative $\big($rigid$\big)$ superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14248 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The algebraic and geometric classification of noncommutative Jordan superalgebras Abdelwahab, Hani Kaygorodov, Ivan Khudoyberdiyev, Abror Rings and Algebras The algebraic and geometric classifications of complex $3$-dimensional noncommutative Jordan superalgebras are given. In particular, we obtain the algebraic and geometric classification of $3$-dimensional Kokoris and standard superalgebras, and, due to one-to-one correspondences between suitable superalgebras, we have classifications for generic Poisson-Jordan and generic Poisson superalgebras. As a byproduct, we have the algebraic and geometric classification of the variety of $3$-dimensional anticommutative superalgebras and its principal subvarieties: Lie, Malcev, binary Lie, Tortkara, anticommutative $\mathfrak{CD}$-, $\mathfrak{s}_4$-, anticommutative terminal superalgebras, anticommutative conservative and anticommutative quasi-conservative $\big($rigid$\big)$ superalgebras. |
| title | The algebraic and geometric classification of noncommutative Jordan superalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2602.14248 |