THE MULTIPLIER AND THE COVER OF DIRECT SUMS OF LIE ALGEBRAS

Abstract

In this paper, we prove that the Schur multiplier of the direct sum of two arbitrary Lie algebras is isomorphic to the direct sum of the Schur multipliers of the direct factors and the usual tensor product of the Lie algebras, which is similar to the work of Miller (1952) in the group case. Also, a cover for the direct sum of two Lie algebras in terms of given covers of them will be constructed.