  We determine the central extensions of a whole family of Lie algebras,
obtained by the method of graded contractions from so(N+1), N arbitrary. All
the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this
family, as well as a large number of other non-semisimple algebras, all of
which have at least a semidirect structure (in some cases two or more). The
dimensions of their second cohomology groups H^2(G,R) and the explicit
expression of their central extensions are given.
