Abstract
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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Arabyani, H. Some properties of the c-nilpotent multiplier of a pair of Lie algebras. Indian J Pure Appl Math 51, 557–564 (2020). https://doi.org/10.1007/s13226-020-0416-6
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DOI: https://doi.org/10.1007/s13226-020-0416-6