On the Nilpotency of a Pair of Lie Algebras
AbstractIn this paper, we introduce the new concepts of nilpotency, upper and lower central series for a pair of Lie algebras $(L,N)$, in which $N$ is an ideal of Lie algebra $L$. We study the properties of these concepts and prove the analogue of Robinson
Theorem for a pair of Lie algebras plays an important role to find the results connecting to the idea of nilpotency in the pair of Lie algebras. In particular we find a criterion such that an extension of pair of Lie algebras can be nilpotent.