Submission: 2012, Jul 19
An exposition is given of the theory of central simple algebras with involution over (formally) real fields. This includes a new proof of Pfister's Local-Global Principle in this setting and the study of related problems.
2010 Mathematics Subject Classification: 11E04, 11E10, 11E81, 12D15, 16K20, 16W10.
Keywords and Phrases: algebra with involution, quaternion algebra, quadratic form, hy- perbolicity, real field, signature, torsion in Witt group, local-global
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