Orthogonal Pfister involutions in characteristic two |
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Authors: | Andrew Dolphin |
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Affiliation: | 1. ICTEAM Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium;2. Fachbereich Mathematik und Statistik, Universität Konstanz, Germany |
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Abstract: | We show that over a field of characteristic 2 a central simple algebra with orthogonal involution that decomposes into a product of quaternion algebras with involution is either anisotropic or metabolic. We use this to define an invariant of such orthogonal involutions that completely determines the isotropy behaviour of the involution. We also give an example of a non-totally decomposable algebra with orthogonal involution that becomes totally decomposable over every splitting field of the algebra. |
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Keywords: | 11E39 11E81 12F05 12F10 |
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