On Characterizing Pairs of Non-Abelian Nilpotent and Filiform Lie Algebras by their Schur Multipliers

Let l be an n-dimensional non-abelian nilpotent lie algebra. niroomand and russo (2011) proved that dimm(l) = 1 2 (n − 1)(n − 2) + 1 − s(l), where m(l) is the schur multiplier of l and s(l) is a non-negative integer. they also characterized the structure of l, when s(l) = 0. assume that (n, l) is a pair of finite dimensional nilpotent lie algebras, in which l is non-abelian and n is an ideal in l and also m(n, l) is the schur multiplier of the pair (n, l). if n admits a complement k say, in l such that dimk = m, then dimm(n, l) = 1 2 (n^2 + 2nm − 3n − 2m + 2) + 1 − (s(l) − t(k)), where t(k) = 1 2m(m − 1)−dimm(k). in the present paper, we characterize the pairs (n, l), for which 0 ≤ t(k) ≤ s(l) ≤3. in particular, we classify the pairs (n, l) such that l is a non-abelian filiform lie algebra and 0 ≤ t(k) ≤ s(l) ≤ 17.