A Local-global Principle for Algebras with Involution and Hermitian Forms
نویسنده
چکیده
Weakly hyperbolic involutions are introduced and a proof is given of the following local-global principle: a central simple algebra with involution of any kind is weakly hyperbolic if and only if its signature is zero for all orderings of the ground field. Also, the order of a weakly hyperbolic algebra with involution is a power of two, this being a direct consequence of a result of Scharlau. As a corollary an analogue of Pfister’s local-global principle is obtained for the Witt group of hermitian forms over an algebra with involution.
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