The concept of the Schur multiplier of a Lie algebra was introduced by Batten et al. (1996). This concept was extended to that of a c-nilpotent multiplier of a Lie algebra, and then further extended to a theory of a c-nilpotent multiplier of a pair of Lie algebras, by the author and others. In this paper we present some new inequalities for the dimension of the c-nilpotent multiplier of a pair of Lie algebras. We also give a necessary and sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to embed into the c-nilpotent multiplier of their quotient. Finally we provide a sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to be finite dimensional.

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一对李代数的c次幂乘子的一些性质

巴顿等人介绍了李代数的舒尔乘数的概念。（1996）。作者和其他人将此概念扩展到李代数的c次幂乘子的概念，然后进一步扩展到对李代数的c次幂乘子的理论。在本文中，我们为一对李代数的c次幂乘子的维数提供了一些新的不等式。我们也给了一个充分必要条件ç一对李代数的-nilpotent乘数嵌入到Ç其商数-nilpotent乘数。最后，我们提供了一个充分条件Ç对李代数的零幂乘子是有限维的。