Recursive Moving Frames for Lie Pseudo-Groups

  • Peter J. Olver
  • Francis Valiquette


This paper introduces a new, fully recursive algorithm for computing moving frames and differential invariants of Lie pseudo-group actions. The recursive method avoids unwieldy symbolic expressions that complicate the treatment of large scale applications of the equivariant moving frame method. The development leads to novel results on partial moving frames, structure equations, and new differential operators underlying the moving frame construction. In particular, our methods produce a streamlined computational algorithm for determining moving frames and differential invariants of finite-dimensional Lie group actions.


Differential invariant lie pseudo-group Maurer–Cartan form moving frame recurrence formula 

Mathematics Subject Classification

53A55 58A15 58A20 58H05 58J70 



We would like to thank the referees for their careful reading of the paper, which led to a considerable improvement in the exposition as well as corrections to the original version.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsSUNY at New PaltzNew PaltzUSA

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