On formal theory of differential equations. III. (English) Zbl 0728.58041

Chrastina, Jan

Math. Bohem. 116, No. 1, 60-90 (1991).

The paper continues the author’s investigations on so-called diffieties (the infinite prolongations of general systems of PDE) [see part I, II of this paper, Čas. Pěstování Mat. 111, 353-383 (1986; Zbl 0638.35008), ibid. 114, 60-105 (1989; Zbl 0703.34001)]; the aim is to develop the elements of general theory of Lie-Cartan pseudogroups with regard of the fact that the study of pseudogroups with the help of diffieties is independent of any particular realization by transformations of a geometrical object. The relations with the equivalence problem, theory of geometrical objects and connection theory are briefly discussed.

Reviewer: Yu.V.Rogovchenko (Kiev)

MSC:

58H05	Pseudogroups and differentiable groupoids
22E65	Infinite-dimensional Lie groups and their Lie algebras: general properties

Keywords:

diffieties; Lie-Cartan pseudogroups; equivalence problem