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


SIGMA 1 (2005), 006, 14 pages      math-ph/0508016      http://dx.doi.org/10.3842/SIGMA.2005.006

Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches

Oleg I. Morozov
Moscow State Technical University of Civil Aviation, 125993 Moscow, Russia

Received August 08, 2005, in final form September 29, 2005; Published online October 13, 2005

Abstract
In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation.

Key words: Lie pseudo-groups; Maurer-Cartan forms; structure equations; symmetries of differential equations.

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