The Poincaré group is the group of isometries of Minkowski spacetime, which includes translations in time and space, as well as Lorentz transformations that combine rotations and boosts. This group plays a crucial role in physics, particularly in the theory of relativity, by describing the symmetries of spacetime and the behavior of particles moving within it. The significance of the Poincaré group extends to Riemannian geometry, especially when examining homogeneous spaces and isometry groups.
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