|
Generalized differential Galois theory
Author(s):
Peter
Landesman
Journal:
Trans. Amer. Math. Soc.
360
(2008),
4441-4495.
MSC (2000):
Primary 13N99
Posted:
March 20, 2008
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field extension.
References:
-
- 1.
- Cassidy, P. J. Differential algebraic groups. Amer. J. Math. 94 (1972), 891-954. MR 0360611
- 2.
- Cassidy, Phyllis J. and Singer, Michael F., Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups, arXiv.math.CA/0502396.
- 3.
- Drach, J. Essai sur la théorie générale de l'itération et sur la classification des transcendantes, Ann. Sci. École Norm. Sup. (3) 15 (1898), 243-384. MR 1508959
- 4.
- Johnson, Joseph; Reinhart, Georg M.; Rubel, Lee A. Some counterexamples to separation of variables. J. Differential Equations 121 (1995), no. 1, 42-66. MR 1348535 (96g:35006)
- 5.
- Kovacic, Jerald J. Differential schemes. Differential algebra and related topics (Newark, NJ, 2000), 71-94, World Sci. Publishing, River Edge, NJ, 2002. MR 1921695 (2003i:12010)
- 6.
- Kovacic, Jerald J. The differential Galois theory of strongly normal extensions. Trans. Amer. Math. Soc. 355 (2003), no. 11, 4475-4522 (electronic). MR 1990759
- 7.
- Kolchin, E. R. Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. (2) 49 (1948), 1-42. MR 0024884 (9:561c)
- 8.
- Kolchin, E. R. Picard-Vessiot theory of partial differential fields, Proc. Amer. Math. Soc. 3 (1952), 596-603. MR 0049883 (14:241c)
- 9.
- Kolchin, E. R. Galois theory of differential fields, Amer. J. Math. 75 (1953), 753-824. MR 0058591 (15:394a)
- 10.
- Kolchin, E. R. On the Galois theory of differential fields, Amer. J. Math. 77 (1955), 868-894. MR 0073588 (17:455a)
- 11.
- Kolchin, E. R. Algebraic groups and algebraic dependence. Amer. J. Math. 90 (1968), 1151-1164. MR 0240106
- 12.
- Kolchin, E. R. Differential algebra and algebraic groups. Pure and Applied Mathematics, Vol. 54. Academic Press, New York-London, 1973. xviii+446 pp. MR 0568864
- 13.
- Kolchin, E. R. Differential algebraic groups. Pure and Applied Mathematics, 114. Academic Press, Inc., Orlando, FL, 1985. xvii+271 pp. ISBN: 0-12-417640-2 MR 0776230 (87i:12016)
- 14.
- Landesman, Peter. Generalized Differential Galois Theory. Ph.D. Thesis, City University of the City of New York, 2006.
- 15.
- Lang, Serge. Introduction to algebraic geometry. Interscience Publishers, Inc., New York-London, 1958, xi+260 pp. MR 0100591
- 16.
- Pillay, A. Algebraic
 -groups and differential Galois theory, Pacific J. Math. 216 (2004), no. 2, 343-360. MR 2094550 (2005k:12007) - 17.
- Pillay, A. Differential Galois theory. I, Illinois J. Math. 42 (1998), no. 4, 678-699. MR 1649893 (99m:12009)
- 18.
- Pillay, A. Differential Galois theory. II, Ann. Pure Appl. Logic 88 (1997), no. 2-3, 181-191. MR 1600903 (99m:12010)
- 19.
- Pommaret, J.-F. Differential Galois theory, Gordon & Breach, New York, 1983. MR 0720863 (85m:12004)
- 20.
- Sit, William Yu. Differential algebraic subgroups of
 and strong normality in simple extensions. Amer. J. Math. 97 (1975), no. 3, 627-698. MR 0396513 - 21.
- Sit, W. Differential dimension polynomials of finitely generated extensions, Proc. Amer. Math. Soc. 68 (1978), no. 3, 251-257. MR 0480353 (81f:12017)
- 22.
- Umemura, H. Galois theory of algebraic and differential equations, Nagoya Math. J. 144 (1996), 1-58. MR 1425591 (98c:12009)
- 23.
- Umemura, H. Differential Galois theory of infinite dimension, Nagoya Math. J. 144 (1996), 59-135. MR 1425592 (98c:12010)
- 24.
- Vessiot, Ernest. Sur la théorie de Galois et ses diverses generalisations. (French) Ann. Sci. École Norm. Sup. (3) 21 (1904), 9-85. MR 1509036
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
13N99
Retrieve articles in all Journals with MSC
(2000):
13N99
Additional Information:
Peter
Landesman
Affiliation:
Department of Mathematics, The Graduate Center of The City University of New York, New York, New York 10016
Email:
mathmaze@yahoo.com
DOI:
10.1090/S0002-9947-08-04586-8
PII:
S 0002-9947(08)04586-8
Received by editor(s):
June 4, 2007
Received by editor(s) in revised form:
July 10, 2007
Posted:
March 20, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
|
Comments: webmaster@ams.org