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Orthogonal Pfister involutions in characteristic two
Authors:Andrew Dolphin
Affiliation:1. ICTEAM Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium;2. Fachbereich Mathematik und Statistik, Universität Konstanz, Germany
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.
Keywords:11E39   11E81   12F05   12F10
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