2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185959We 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.Latex file. 32 pages. Minor changes. To appear in J. Phys. AQuantum AlgebraHigh Energy Physics - TheoryMathematical Physicstext