Recursive Moving Frames for Lie Pseudo-Groups

Peter J. Olver, Francis Valiquette

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Article number57
JournalResults in Mathematics
Issue number2
StatePublished - Jun 1 2018

Bibliographical note

Funding Information:
Peter J. Olver was supported in part by NSF Grant DMS 11–08894. Francis Valiquette was supported in part by an AARMS Postdoctoral Fellowship.

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.


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


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