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Quaternion algebras with derivations
Authors:Amit Kulshrestha  Varadharaj R. Srinivasan
Affiliation:1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-40005, India;2. Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University, Japan;3. Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-Ku, Tokyo 156-0045, Japan;1. Department of Mathematics, University of Oregon, Eugene, OR, USA;2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada;3. Department of Pure Mathematics, University of Waterloo & Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada;1. Dipartimento di Informatica, Università degli Studi di Verona, Strada le Grazie 15, 37134 Verona, Italy;2. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, 3000 Sfax, Tunisia
Abstract:We study derivations on quaternion algebras that stabilise quadratic subfields. Following the work of L. Juan and A. Magid [10], we provide an explicit construction of a differential splitting field for a given differential quaternion algebra. We also examine the presence and impact of those derivations on quaternion algebras that admit new constants.
Keywords:Differential fields  Quaternion algebras
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