Characterization of relative n-isoclinism of Lie algebras

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}.

Keywords:

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