Lie Completion of Pseudo-Groups

نویسندگان

  • Vladimir Itskov
  • Peter J. Olver
  • Francis Valiquette
چکیده

By far the most important class of pseudo-groups, for both 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. Supported in part by NSF Grant 08–07317. Supported by a University of Minnesota Graduate School Doctoral Dissertation Fellowship and NSF Grant 05–05293.

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تاریخ انتشار 2009