Strongly anisotropic involutions on central simple algebras
(2011) Communications in Algebra — Vol. 39, n° 5, p. 1686-1704 (2011)
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- Abstract
- The classical theorem of Bröcker and Prestel on quadratic forms over formally real fields determines a valuation theoretic condition under which all totally indefinite forms are weakly isotropic. In this article, we look for analogues of such a result in a more general setting of algebras with involutions. We prove that for involutions of first kind over central simple algebras of index two, one indeed has a Bröcker-Prestel like statement. The connection between two conditions, namely, total indefiniteness and weak isotropy is made via so called gauge functions on central simple algebras. © Taylor & Francis Group, LLC.
Citations
Kulshrestha, A. (2011). Strongly anisotropic involutions on central simple algebras. Communications in Algebra, 39(5), 1686-1704. https://doi.org/10.1080/00927871003739012 (Original work published 2011)