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
Full text: dvi.gz 18 k, dvi 42 k, ps.gz 81 k, pdf.gz 65 k, pdf 101 k.