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arXiv · 2210.02103

Splitting of differential quaternion algebras

Parul Gupta·Yashpreet Kaur·Anupam Singh
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Abstract

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.

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Parul Gupta, Yashpreet Kaur, Anupam Singh. 2022-10-05. Splitting of differential quaternion algebras. https://doi.org/10.1016/j.jalgebra.2023.06.022

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