微分伽罗瓦理论
概述
编辑代数伽罗瓦理论研究代数域的扩张， 而微分伽罗瓦理论则研究微分域的扩张，即具备导子D的域。这两种构造的一个区别是，微分伽罗瓦理论中的伽罗瓦群往往是矩阵李群，而代数伽罗瓦理论中常常是有限群。
另见
编辑参考文献
编辑- Hubbard, John H.; Lundell, Benjamin E. A First Look at Differential Algebra (PDF). The American Mathematical Monthly. 2011, 118 (3): 245–261 [2024-02-15]. JSTOR 10.4169/amer.math.monthly.118.03.245. S2CID 1567399. doi:10.4169/amer.math.monthly.118.03.245. （原始内容存档 (PDF)于2017-09-22）.
- Bertrand, D., Review of "Lectures on differential Galois theory" (PDF), Bulletin of the American Mathematical Society, 1996, 33 (2) [2024-02-15], ISSN 0002-9904, doi:10.1090/s0273-0979-96-00652-0
, （原始内容存档 (PDF)于2006-05-18） - Beukers, Frits, 8. Differential Galois theory, Waldschmidt, Michel; Moussa, Pierre; Luck, Jean-Marc; Itzykson, Claude (编), 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: 413–439, 1992, ISBN 3-540-53342-7, Zbl 0813.12001
- Magid, Andy R., Lectures on differential Galois theory, University Lecture Series 7, Providence, R.I.: American Mathematical Society, 1994, ISBN 978-0-8218-7004-4, MR 1301076
- Magid, Andy R., Differential Galois theory (PDF), Notices of the American Mathematical Society, 1999, 46 (9): 1041–1049 [2024-02-15], ISSN 0002-9920, MR 1710665, （原始内容存档 (PDF)于2024-08-11）
- van der Put, Marius; Singer, Michael F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 328, Berlin, New York: Springer-Verlag, 2003 [2024-02-15], ISBN 978-3-540-44228-8, MR 1960772, （原始内容存档于2017-12-26）
- Juan J. Morales Ruiz : Differential Galois Theory and Non-Integrability of Hamiltonian Systems, Birkhaeuser, 1999, ISBN 978-3764360788 .
