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Abstract
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Using a recursive metho d, we study the structure of a Lie pse udo-group action which was intro duced
by Cartan. Lie pseudo-groups are the infinite-dimensional counterparts of lo cal Lie group actions. We
asso ciate a system of PDEs to the pseudo-group action, which called determining e quations of the pseudogroup action, we obtain the diffe re ntial invariants, invariant differential form s and recurrence relations
among them for the Lie pseudo-group action. The invariant differential forms provide a complete system
of functionally indep e ndent invariant differential forms that c an b e used to solve the e quivalence problem.
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