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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2501.18654 |
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| _version_ | 1866912211680624640 |
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| author | Hernández, Isabel Martin, María Eugenia Rodrigues, Rodrigo Lucas |
| author_facet | Hernández, Isabel Martin, María Eugenia Rodrigues, Rodrigo Lucas |
| contents | We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras, respectively. In both cases, the irreducible components of the varieties are described. Furthermore, we exhibit a four-dimensional solvable rigid Jordan superalgebra, showing that an analogue to the Vergne conjecture for Jordan superalgebras does not hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible Components of the Varieties of Jordan Superalgebras of Types $(1,3)$ and $(3,1)$ Hernández, Isabel Martin, María Eugenia Rodrigues, Rodrigo Lucas Rings and Algebras We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras, respectively. In both cases, the irreducible components of the varieties are described. Furthermore, we exhibit a four-dimensional solvable rigid Jordan superalgebra, showing that an analogue to the Vergne conjecture for Jordan superalgebras does not hold. |
| title | Irreducible Components of the Varieties of Jordan Superalgebras of Types $(1,3)$ and $(3,1)$ |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.18654 |