Abstract
The general solution of the graded contraction equations for a grading of the real compact simple Lie algebra so(N+1) is presented in an explicit way. It turns out to depend on independent real parameters. The structure of the general graded contractions is displayed for the low-dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes.
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