On covers of lie algebras

Abstract In dealing with the central extensions of a finite group G one finds that although covers need not be isomorphic, for each such H there exists a cover for which H is a. homomorphic image 1. For finite dimensional Lie algebras, covers are isomorphic. We shall show that the second property also holds for Lie algebras. Thus to find all such extensions one needs to compute the cover and consider ideals contained in the multiplier (kernel of the homomorphism). Several examples are constructed. Our Lie algebras are taken over a field.