On Schur Multiplier of a Pair of Lie Algebras

Nilpotent Lie algebras have played an important role in mathematics in the classification theory ofLie algebras. Let (N, L) be a pair of finite dimensional Lie algebras. Let K be an ideal of L suchthat L = N ⊕ K and N be a filiform ideal of L. Also, let dim N = n and dim K = m. Thens′(N, L) = ۱/۲(n − ۱)(n − ۲) + ۱ + (n − ۱)m − dim M(N, L). In this paper, we characterize the pair(N, L) for s′(N; L) = ۰, ۱, ۲,..., ۱۵.