Summary
The theory of Lie transformation groups is extended to a theory of extended Lie transformation groups by extending the group parameters to functions of coordinates in the base manifolds. The result is global both in the group manifolds (the O. Schreier's fundamental theorems being not taken into account) as well as in the base differentiable manifolds owing to the introduction of the author'sII-geodesic parallel coordinates. The Lie's fundamental theorems are extremely simplified.
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Takasu, T. A theory of extended lie transformation groups. Annali di Matematica 61, 247–333 (1963). https://doi.org/10.1007/BF02410654
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DOI: https://doi.org/10.1007/BF02410654