David W. Lewis, Thomas Unger: A local-global principle for algebras with involution and hermitian forms

david.lewis@ucd.ie, thomas.unger@ucd.ie

Submission: 2001, Oct 4

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.

2000 Mathematics Subject Classification: 16K20, 11E39

Keywords and Phrases: Central simple algebras, involutions, hermitian forms, local-global principle

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