Differential Galois theory

Short description: Study of Galois symmetry groups of differential fields

In mathematics, differential Galois theory studies the Galois groups of differential equations.

## Overview

Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. fields that are equipped with a derivation, D. Much of the theory of differential Galois theory is parallel to algebraic Galois theory. One difference between the two constructions is that the Galois groups in differential Galois theory tend to be matrix Lie groups, as compared with the finite groups often encountered in algebraic Galois theory.

## See also

* Picard–Vessiot theory

## References

* Hubbard, John H.; Lundell, Benjamin E. (2011). "A First Look at Differential Algebra". The American Mathematical Monthly 118 (3): 245–261. doi:10.4169/amer.math.monthly.118.03.245. http://www.math.cornell.edu/~hubbard/diffalg1.pdf.
* Bertrand, D. (1996), "Review of "Lectures on differential Galois theory"", Bulletin of the American Mathematical Society 33 (2), doi:10.1090/s0273-0979-96-00652-0, ISSN 0002-9904, http://www.ams.org/bull/1996-33-02/S0273-0979-96-00652-0/S0273-0979-96-00652-0.pdf
* Beukers, Frits (1992), "8. Differential Galois theory", in Waldschmidt, Michel; Moussa, Pierre; Luck, Jean-Marc et al., From number theory to physics. Lectures of a meeting on number theory and physics held at the Centre de Physique, Les Houches (France), March 7–16, 1989, Berlin: Springer-Verlag, pp. 413–439, ISBN 3-540-53342-7
* Magid, Andy R. (1994), Lectures on differential Galois theory, University Lecture Series, 7, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-7004-4, https://books.google.com/books?id=cJ9vByhPqQ8C
* Magid, Andy R. (1999), "Differential Galois theory", Notices of the American Mathematical Society 46 (9): 1041–1049, ISSN 0002-9920, http://www.ams.org/notices/199909/fea-magid.pdf
* van der Put, Marius; Singer, Michael F. (2003), Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 328, Berlin, New York: Springer-Verlag, ISBN 978-3-540-44228-8, http://www4.ncsu.edu/~singer/ms_papers.html

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