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

 

Picard-Vessiot extensions for real fields


Author: Elżbieta Sowa
Journal: Proc. Amer. Math. Soc. 139 (2011), 2407-2413
MSC (2010): Primary 12H05; Secondary 12F10, 12D15
Published electronically: December 9, 2010
MathSciNet review: 2784805
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Abstract: We define a notion of Picard-Vessiot extension for a homogeneous linear differential equation $ \mathcal{L}=0$ defined over a real differential field $ K$ with a real closed field of constants $ C_{K}$. When $ \mathcal{L}$ has differential Galois group $ GL_{n}$ over the complexification of $ K$, we prove that a Picard-Vessiot extension for $ \mathcal{L}$ exists over $ K$.


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Additional Information

Elżbieta Sowa
Affiliation: Instytut Matematyki i Informatyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, 30-348 Kraków, Poland
Email: elzbieta.sowa@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10700-1
PII: S 0002-9939(2010)10700-1
Received by editor(s): September 17, 2009
Received by editor(s) in revised form: March 19, 2010, and July 2, 2010
Published electronically: December 9, 2010
Additional Notes: This work was supported by the Polish Grant N20103831/3261
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.