Explicit isomorphisms of quaternion algebras over quadratic global fields

2020/07/14 by Csahók, Tímea, Kutas, Péter, Montessinos, Mickaël +1
#FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2007.06981

Abstract

Let L be a separable quadratic extension of either ℚ or \mathbbF_q(t). We propose 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.

Related

• Quadratic Extension Algebras and Quaternion Algebras Over Fields (of Characteristic not 2)
• Total linkage of quaternion algebras and Pfister forms in characteristic\n two
• Transfer of quadratic forms and of quaternion algebras over quadratic field extensions
• On quaternion algebras over some extensions of quadratic number fields
• On quaternion algebras that split over quadratic number fields