On the Local Theory of Continuous Infinite Pseudo Groups I

Author:

Kuranishi Masatake

Abstract

The local theory of continuous (infinite) pseudo-groups of transformations was originated by S. Lie, and developed by himself, F. Engel, E. Vessiot, E. Cartan, etc. In the beginning, the definition was not clear and we can find several different definitions in the papers of pioneers. In 1902, E. Cartan introduced a definition using his theory of exterior differential systems and made an extensive study in his series of papers [1], [2], and [31 The writer will adopt his definition in this series of papers. A continuous pseudo-group of transformations is, roughly speaking, a collection of real (or complex) analytic homeo-morphisms of domains in a real (or complex) euclidean space, which is closed under the operations of composition and inverse, and which forms the general solutions of a system of partial differential equations.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference4 articles.

1. Sur la structure des groupes infinis de transformation

2. Les sous-groupes des groupes continus de transformations;Cartan;ibid,1908

3. Les groupes de transformations continus;Cartan;infinis, simples, ibid,1909

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