The aim of this paper is to introduce the concept of the Schur multiplier M(L, N) of a pair of Lie algebras and to obtain some inequalities for the dimension of M(L, N). Also, we consider some of the features of central extension of an arbitrary Lie algebra. Moreover, we present a necessary and sufficient condition in which the Schur multiplier of a pair of Lie algebras can be embedded into the Schur multiplier of their factor Lie algebras.
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