Article ID Journal Published Year Pages File Type
4596294 Journal of Pure and Applied Algebra 2014 16 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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