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Picard-Vessiot theory for real fields |
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| Authors: | Teresa Crespo Zbigniew Hajto El?bieta Sowa |
| Institution: | 1. Departament d’ àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain 2. Faculty of Mathematics and Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30-348, Kraków, Poland 3. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Kraków, Poland |
| Abstract: | The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we prove the existence of a Picard-Vessiot extension for a homogeneous linear differential equation defined over a real differential field K with real closed field of constants. We give an adequate definition of the differential Galois group of a Picard-Vessiot extension of a real differential field with real closed field of constants and we prove a Galois correspondence theorem for such a Picard-Vessiot extension. |
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