Explicit isomorphisms of quaternion algebras over quadratic global fields

Csahók, Tímea and Kutas, Péter and Montessinos, Mickaël and Zábrádi, Gergely (2022) Explicit isomorphisms of quaternion algebras over quadratic global fields. RESEARCH IN NUMBER THEORY, 8 (4). ISSN 2363-9555

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Abstract

Let L be a separable quadratic extension of either {\mathbb {Q}} Q or {\mathbb {F}}_q(t) F q ( t ) . We exhibit efficient algorithms for finding isomorphisms between quaternion algebras over L . Our techniques are based on computing maximal one-sided ideals of the corestriction of a central simple L -algebra.

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