Some inequalities for the multiplier of a pair of n-Lie algebras

Abstract

Let [Formula: see text] be a pair of [Formula: see text]-Lie algebras. Then, we introduce the concept of Schur multiplier of the pair [Formula: see text], denoted by [Formula: see text], and some inequalities for the dimension of [Formula: see text] are given. We also determine a necessary and sufficient condition, for which the Schur multiplier of a pair of [Formula: see text]-Lie algebras can be embedded into the Schur multipliers of their [Formula: see text]-Lie algebra factors. Moreover, some inequalities for the Schur multiplier of a pair of finite-dimensional nilpotent [Formula: see text]-Lie algebras are acquired.