Two Algorithms for a Moving Frame Construction

The method of moving frames, introduced by Elie Cartan, is a powerful tool for constructing invarinats and solving various equivalence problems. The practical implementation of Cartan's method, however, remains to be challenging, despite its later significant development and generalization.

I will present two variations on the Fels and Olver algorithm, which under some conditions on the group action, simplify a moving frame construction. In addition, the first algorithm leads to a better understanding of invariant differential forms on the jet bundles, while the second expresses the differential invariants for the entire group in terms of the differential invariants of its subgroup.