Lie Completion of Pseudo-Groups

  title={Lie Completion of Pseudo-Groups},
  author={Vladimir Itskov and Peter J. Olver and Francis Valiquette},
By far the most important class of pseudo-groups, both for theory and in essentially all applications, are the Lie pseudo-groups. In this paper we propose a definition of the Lie completion of a regular pseudo-group, and establish some of its basic properties. In particular, a pseudo-group and its Lie completion have exactly the same differential invariants and invariant differential forms. Thus, for practical purposes, one can exclusively work within the category of Lie pseudo-groups.