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Differential Galois theory of infinite dimension

Published online by Cambridge University Press:  22 January 2016

Hiroshi Umemura
Hiroshi Umemura*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan, email: umemura@math.nagoya-u.ac.jp
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This paper is the second part of our work on differential Galois theory as we promised in [U3]. Differential Galois theory has a long history since Lie tried to apply the idea of Abel and Galois to differential equations in the 19th century (cf. [U3], Introduction). When we consider Galois theory of differential equation, we have to separate the finite dimensional theory from the infinite dimensional theory. As Kolchin theory shows, the first is constructed on a rigorous foundation. The latter, however, seems inachieved despite of several important contributions of Drach, Vessiot,…. We propose in this paper a differential Galois theory of infinite dimension in a rigorous and transparent framework. We explain the idea of the classical authors by one of the simplest examples and point out the problems.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 144 , December 1996 , pp. 59 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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