Splitting of differential quaternion algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866909158076317696 |
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| author | Gupta, Parul Kaur, Yashpreet Singh, Anupam |
| author_facet | Gupta, Parul Kaur, Yashpreet Singh, Anupam |
| contents | We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$. However, a differential quaternion algebra need not be split over any algebraic extension of $k$. We use solutions of certain Riccati equations to provide bounds on the transcendence degree of splitting fields of a differential quaternion algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02103 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Splitting of differential quaternion algebras Gupta, Parul Kaur, Yashpreet Singh, Anupam Rings and Algebras 12H05, 16H05, 16W25 We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$. However, a differential quaternion algebra need not be split over any algebraic extension of $k$. We use solutions of certain Riccati equations to provide bounds on the transcendence degree of splitting fields of a differential quaternion algebra. |
| title | Splitting of differential quaternion algebras |
| topic | Rings and Algebras 12H05, 16H05, 16W25 |
| url | https://arxiv.org/abs/2210.02103 |