Banafshe Vesi - Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

In 1994, Moneyhun introduced and studied the concept of isoclinism in Lie algebras.Moghaddam and parvaneh in 2009 introduced and gave some properties of isoclinism of a pairof Lie algebras. In this paper we introduce the concept of relative n-isoclinism between twopairs of Lie algebras. They form equivalence classes and we show that each equivalent classcontains an n-stem pair of Lie algebras. We also show that for a relative n-isoclinism family ofLie algebras C say, consists of (M, L) such that L is finitely generated and [Mm L] is finitedimension, then there exists an n-stem pair of Lie algebras (R, S) ε C such thatdim([Rm-1 S] = min{dim([M m-1 L]); forall(M,L) ε C}.

Lie algebra, n-isoclinism, relative n-isoclinism, n-stem Lie algebra