Submission: 2013, Aug 7
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 in characteristic 2 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.
2010 Mathematics Subject Classification: 11E39, 11E81, 12F05, 12F10
Keywords and Phrases: Central simple algebras; quaternion algebras; involutions; Pfister forms; characteristic two, Pfister Factor Conjecture.
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