Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 077, 14 pages      arXiv:0907.4086
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

On the Structure of Lie Pseudo-Groups

Peter J. Olver a, Juha Pohjanpelto b and Francis Valiquette a
a) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
b) Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA

Received March 31, 2009, in final form July 08, 2009; Published online July 23, 2009

We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical and practical standpoint.

Key words: Lie pseudo-group; infinitesimal generator; jet; contact form; Maurer-Cartan form; structure equations; essential invariant.

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