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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2411.18996 |
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| _version_ | 1866915039552733184 |
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| author | Tambara, Daisuke |
| author_facet | Tambara, Daisuke |
| contents | Let $A$ be a three-dimensional nonassociative division algebra over a finite field. Let $A$ act on the space $A^2$ by left multiplication. For a nonzero vector $v$ in $A^2$ we have a three-dimensional subspace $Av$ in $A^2$. This paper concerns about possible dimension of the intersection of $Av$ and $Av'$ for $v, v'$ in $A^2$. One of our results is that there exists a two-dimensional intersection if and only if $A$ is isotopic to a commutative algebra. We use a classical theorem that A is a twisted field of Albert. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection of subspaces in $A^2$ for a three-dimensional division algebra $A$ over a finite field Tambara, Daisuke Rings and Algebras 17A35, 12E20 Let $A$ be a three-dimensional nonassociative division algebra over a finite field. Let $A$ act on the space $A^2$ by left multiplication. For a nonzero vector $v$ in $A^2$ we have a three-dimensional subspace $Av$ in $A^2$. This paper concerns about possible dimension of the intersection of $Av$ and $Av'$ for $v, v'$ in $A^2$. One of our results is that there exists a two-dimensional intersection if and only if $A$ is isotopic to a commutative algebra. We use a classical theorem that A is a twisted field of Albert. |
| title | Intersection of subspaces in $A^2$ for a three-dimensional division algebra $A$ over a finite field |
| topic | Rings and Algebras 17A35, 12E20 |
| url | https://arxiv.org/abs/2411.18996 |