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Keywords:
Lie-Cartan pseudogroups; diffieties; equivalence problem; Cauchy characteristics; composition series; geometrical object
Lie-Cartan pseudogroups; diffieties; equivalence problem; Cauchy characteristics; composition series; geometrical object
Summary:
Elements of the general theory of Lie-Cartan pseudogroups (including the intransitive case) are developed within the framework of infinitely prolonged systems of partial differential equations (diffieties) which makes it independent of any particular realizations by transformations of geometric object. Three axiomatic approaches, the concepts of essential invariant, subgroup, normal subgroup and factorgroups are discussed. The existence of a very special canonical composition series based on Cauchy characteristics is proved and relations to the equivalence problem, theory of geometrical objects and connection theory are briefly mentioned.
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