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S. Lie discovered in 1890 the "Lie pseudogroups", namely the groups of transformations solutions of systems of partial differential (PD) equations. During the next fifty years, these groups have only been studied by E. Cartan and E. Vessiot but the "Vessiot structure equations" are still unknown today. In the meantime, a "formal theory" of systems of PD equations has been pioneered by M. Janet in 1920. Then, the physicists E. Inonu and E.P. Wigner introduced in 1953 the concept of "deformation of a Lie algebra" by considering the speed of light as a parameter in the Lorentz composition of...