Finite linear groups as differential Galois groups

• Autorzy: Crespo, T. , Hajto, Z.
• Języki publikacji: EN

Abstrakty

EN

An effective construction of linear differential equations with Galois group a given finite group is presented.

Słowa kluczowe

PL

grupa Galois; reprezentacja grupy; zagadnienie odwrotne

EN

differential Galois group; group representations; inverse problem

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 4
• Strony: 361--373
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Crespo, T.

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland,
• Departament D'Algebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

autor

Hajto, Z.

• Institute of Mathematics, University of Agriculture, Al. Mickiewicza 24/28, 30- 059 Kraków, Poland ,

Bibliografia

• [1] M. Artin, Algebra, Prentice-Hall, Englewood Cliffs, NJ 1991.
• [2] T. Crespo, Z. Hajto, Finite linear groups as differential Galois groups, Prepublicacions de la Universitat Autónoma de Barcelona, no. 11 (1998).
• [3] W. Fulton, J. Harris, Representation theory: a first course, Springer-Verlag, New York 1991.
• [4] I. Kaplansky, An introduction to differential algebra, Hermann, Paris 1976.
• [5] A. R. Magid, Lectures on differential Galois theory, Univ. Lecture Ser., 7 (1994).
• [6] G. Malle, B. H. Matzat, Inverse Galois theory, Springer-Verlag, Berlin 1999.
• [7] J-F. Mestre, Extensions régulières de Q(t) de groupe de Galois Ãn, J. Algebra, 131 (1990) 483-495.
• [8] M. van der Put, F. Ulmer, Differential equations and finite groups, J. Algebra, 226 (2000) 920-966.
• [9] M. F. Singer, An outline of differential Galois theory, in: Computer algebra and differential equations, ed.: E. Tournier, Academic Press, London-New York 1990, 3-57.
• [10] M. F. Singer, F. Ulmer, Galois groups of second and third order linear differential equations, J. Symbolic Comput., 16 (1993) 9-36.
• [11] J. Sonn, Central extensions of Sn as Galois groups of regular extensions of Q(T), J. Algebra, 140 (1991) 355-359.