Splitting of differential quaternion algebras

Parul Gupta; Yashpreet Kaur; Anupam Singh

doi:10.1016/j.jalgebra.2023.06.022

paper

Splitting of differential quaternion algebras

arXiv:2210.02103 · doi:10.1016/j.jalgebra.2023.06.022

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.

References in corpus (1)

Splitting fields of differential symbol algebras