Characterization of relative n-isoclinism of a pair of Lie algebras

Abstract

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 pair of Lie algebras. In this paper we introduce the concept of relative n-isoclinism between two pairs of Lie algebras. They form equivalence classes and we show that each equivalent class contains an n-stem pair of Lie algebras. We also show that for a relative n-isoclinism family of Lie algebras C say, consists of (M, L) such that L is finitely generated and [M, _n L] is finite dimension, then there exists an n-stem pair of Lie algebras (R, S) ∊ C such that ; for all (M, L) ∊ C}.