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 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. A

References in corpus (2)

• Casimir invariants for the complete family of quasi-simple orthogonal algebras
• Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras

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