THE GENERAL-SOLUTION OF THE REAL Z(2)(CIRCLE-TIMES-N) GRADED CONTRACTIONS OF SO(N+1)

The general solution of the graded contraction equations for a Z(2)(xN ) grading of the real compact simple Lie algebra so(N + 1) is presente d in an explicit way. It turns out to depend on 2(N) - 1 independent r eal parameters. The structure of the general graded contractions is di splayed for the low-dimensional cases, and kinematical algebras are sh own to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in part icular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes.