The groups of Poincaré and Galilei in arbitrary dimensional spaces

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Abstract
In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincaré algebra. The usual contraction of the Poincaré to the Galilei group is seen to be equivalent to a certain coordinate transformation.