On Schur Multiplier of a Pair of Lie Algebras

Document Type : Research Paper


Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.


Nilpotent Lie algebras have played an important role in mathematics in the classification theory of
Lie algebras. Let (N, L) be a pair of finite dimensional Lie algebras. Let K be an ideal of L such
that L = N K and N be a filiform ideal of L. Also, let dim N = n and dim K = m. Then
s′(N, L) = 1/2(n − 1)(n − 2) + 1 + (n − 1)m dim M(N, L). In this paper, we characterize the pair
(N, L) for s′(N; L) = 0, 1, 2,..., 15.