Some Remarks on the Infinite de Sitter Space
One can define de Sitter space as a four-dimensional space with the following two properties. First, it is invariant under the operations of a transitive ten-parametric group. Four of the infinitesimal operators of this group are usually made to correspond to the components of the energy-momentum vector, the other six to the angular momentum tensor. Second, the subgroup of this ten-parametric group which leaves a given point of the space invariant must be isomorphic to the ordinary homogeneous Lorentz group. This last point ensures that the neighborhood of any point of these de Sitter spaces behaves like the flat space of special relativity (Minkowski space).
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