Solvable-by-finite groups as differential Galois groups

Claude Mitschi; Michael F. Singer

Annales de la Faculté des sciences de Toulouse : Mathématiques (2002)

  • Volume: 11, Issue: 3, page 403-423
  • ISSN: 0240-2963

How to cite

top

Mitschi, Claude, and Singer, Michael F.. "Solvable-by-finite groups as differential Galois groups." Annales de la Faculté des sciences de Toulouse : Mathématiques 11.3 (2002): 403-423. <http://eudml.org/doc/73584>.

@article{Mitschi2002,
author = {Mitschi, Claude, Singer, Michael F.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Picard-Vessiot extension; differential Galois group; inverse problem of differential Galois theory},
language = {eng},
number = {3},
pages = {403-423},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Solvable-by-finite groups as differential Galois groups},
url = {http://eudml.org/doc/73584},
volume = {11},
year = {2002},
}

TY - JOUR
AU - Mitschi, Claude
AU - Singer, Michael F.
TI - Solvable-by-finite groups as differential Galois groups
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2002
PB - UNIVERSITE PAUL SABATIER
VL - 11
IS - 3
SP - 403
EP - 423
LA - eng
KW - Picard-Vessiot extension; differential Galois group; inverse problem of differential Galois theory
UR - http://eudml.org/doc/73584
ER -

References

top
  1. [1] Bertrand ( D.). - Review of "Lectures on differential Galois theory" by A. Magid, Bull. AMS, 33 (1996), 289-294. Springer Verlag, 1991. MR1466700
  2. [2] Borel ( A.). - Linear Algebraic Groups, second edition, Springer Verlag, 1991. Zbl0726.20030MR1102012
  3. [3] Borel ( A.), Serre ( J.-P.). - Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv., 39 (1964-1965), 111-164. Zbl0143.05901MR181643
  4. [4] Chevalley ( C.). - Théorie des groupes de Lie, Vol.II, Groupes algébriques, Hermann, Paris, 1951. Zbl0054.01303MR51242
  5. [5] Deligne ( P.). - Catégories tannakiennes, The Grothendieck Festschrift2, p. 111-195, Progress in Math., 87 (1990), Birkhäuser. Zbl0727.14010MR1106898
  6. [6] Hartmann ( J.). - On the Inverse Problem in Differential Galois Theory, Preprint, Universität Heidelberg, 2002. 
  7. [7] Hochschild ( G.). - Basic Theory of Algebraic Groups and Lie Algebras, Graduate Texts in Mathematics, 75, Springer-Verlag, 1981. Zbl0589.20025MR620024
  8. [8] Kolchin ( E.R.). - Differential Algebra and Algebraic Groups, Academic Press, 1976. Zbl0264.12102MR568864
  9. [9] Kolchin ( E.R.). - Algebraic groups and algebraic dependence, Amer. J. Math., 90 (1968), 1151-1164. Zbl0169.36701MR240106
  10. [10] Kovacic ( J.). - The Inverse Problem in the Galois Theory of Differential Fields, Annals of Mathematics, 89 (1969), 583-608. Zbl0188.33801MR244218
  11. [11] Kovacic ( J.). - On the Inverse Problem in the Galois Theory of Differential Fields, Annals of Mathematics, 93 (1971), 269-284. Zbl0214.06004MR285514
  12. [12] Lang ( S.). - Algebra, Third Edition, Addison-Wesley, 1993. Zbl0848.13001
  13. [13] Magid ( A.). - Lectures on Differential Galois theory, University Lecture Series, American Mathematical Society, Second edition, 1994. Zbl0855.12001MR1301076
  14. [14] Mitschi ( C.), Singer ( M.F.). - Connected Linear Groups as Differential Galois Groups, Journal of Algebra, 184 (1996), 333-361. Zbl0867.12004MR1402584
  15. [15] Van Der Put ( M.). - Galois Theory of differential equations, algebraic groups and Lie algebras, Journal of Symbolic Computation, 28 (1999), 441-472. Zbl0997.12008MR1731933
  16. [16] Van Der Put ( M.). - Recent work in differential Galois theory, Séminaire Bourbaki, volume 1997/98 (exposé 849), Astérisque, Société Mathématique de France, Paris, 1998. Zbl0931.12008MR1685624
  17. [17] Van Der Put ( M.), Singer ( M.F.).— Galois Theory of Differential Equations, to appear. 
  18. [18] Ritt ( J.F.). - Differential Algebra, Am. Math. Soc. Coll. Pub., Vol. 33, Am. Math.Soc., 1950. Zbl0037.18402MR35763
  19. [19] Ramis ( J.P.). - About the Inverse Problem in Differential Galois Theory: the Differential Abhyankar Conjecture, unpublished manuscript, 1996. MR1443697
  20. [20] Ramis ( J.P.). - About the inverse problem in differential Galois theory: the differential Abhyankar conjecture, in The Stokes phenomenon and Hilbert's 16th Problem, World Scientific Publ. (Editors B.L.J. Braaksma, G.K. Immink, M. van der Put), Singapore1996. Zbl0860.12003MR1443697
  21. [21] Serre ( J.P.).— Cohomologie Galoisienne, cinquième édition, Lecture Notes in Mathematics, 5, Springer-Verlag, 1994. Zbl0812.12002MR1324577
  22. [22] Singer ( M.F.). - Moduli of linear differential equations on the Riemann sphere with fixed Galois groups, Pacific J. Math., 106, No. 2 (1993), 343-395. Zbl0778.12007MR1233356
  23. [23] Tretkoff ( C.), Tretkoff ( M.). - Solution of the inverse problem of differential Galois theory in the classical case, Amer. J. Math., 1979, 1327-1332. Zbl0423.12021MR548884
  24. [24] Volklein ( H.). - Groups as Galois Groups, Cambridge Studies in Advanced Mathematics, Vol. 53, Cambridge University Press, 1996. Zbl0868.12003MR1405612
  25. [25] Wehfritz ( B.A.F.). - Infinite Linear Groups, Springer-Verlag, 1973. Zbl0261.20038

NotesEmbed ?

top

You must be logged in to post comments.