Central extensions of the quasi-orthogonal Lie algebras

Abstract

We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from , 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 and the explicit expression of their central extensions are given.