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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pfister's theorem for orthogonal involutions of degree 12


Authors: Skip Garibaldi and Anne Quéguiner-Mathieu
Journal: Proc. Amer. Math. Soc. 137 (2009), 1215-1222
MSC (2000): Primary 20G15; Secondary 16W10, 11E04
Published electronically: October 2, 2008
MathSciNet review: 2465642
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Abstract: We use the fact that a projective half-spin representation of $ \operatorname{Spin}_{12}$ has an open orbit to generalize Pfister's result on quadratic forms of dimension 12 in $ I^3$ to orthogonal involutions.


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Additional Information

Skip Garibaldi
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: skip@member.ams.org

Anne Quéguiner-Mathieu
Affiliation: Université Paris 13 (LAGA), CNRS (UMR 7539), Université Paris 12 (IUFM), 93430 Villetaneuse, France
Email: queguin@math.univ-paris13.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09674-3
PII: S 0002-9939(08)09674-3
Received by editor(s): April 10, 2008
Published electronically: October 2, 2008
Communicated by: Martin Lorenz
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.