Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 7 2 2022 09 01 On Schur Multiplier of a Pair of Lie Algebras 161 169 325 10.22128/gadm.2022.531.1072 EN Homayoon Arabyani Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. Journal Article 2022 05 03 Nilpotent Lie algebras have played an important role in mathematics in the classification theory of<br />Lie algebras. Let (<em>N, L</em>) be a pair of finite dimensional Lie algebras. Let <em>K</em> be an ideal of <em>L</em> such<br />that <em>L = N </em>⊕<em> K </em>and N be a filiform ideal of <em>L</em>. Also, let dim <em>N = n</em> and dim <em>K = m</em>. Then<br /><em>s′(N, L) = 1/2(n − 1)(n − 2) + 1 + (n − 1)m </em>−<em> dim M(N, L).</em> In this paper, we characterize the pair<br />(<em>N, L</em>) for <em>s′(N; L)</em> = 0, 1, 2,..., 15. https://ansne.du.ac.ir/article_325_43d79850781837cd5a4fa08e99fe230b.pdf