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Lie completion of pseudo-groups

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588, USA

    Vladimir Itskov

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Peter J. Olver

  3. Department of Mathematics and Statistics, McGill University, Montréal, Québec, H3A 2K6, Canada

    Francis Valiquette

Authors
  1. Vladimir Itskov
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  2. Peter J. Olver
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  3. Francis Valiquette
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Corresponding author

Correspondence to Vladimir Itskov.

Additional information

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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Itskov, V., Olver, P.J. & Valiquette, F. Lie completion of pseudo-groups. Transformation Groups 16, 161–173 (2011). https://doi.org/10.1007/s00031-010-9118-1

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  • DOI: https://doi.org/10.1007/s00031-010-9118-1

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