Isoclinic relative extensions of pairs of Lie algebras

Abstract

In the present paper we introduce the concept of isoclinism on the relative central extensions of pairs of Lie algebras, which forms an equivalence relation and we show that each equivalence class contains a stem relative central extension. Also, we determine the structure of all relative central extensions in an isoclinism family of a given relative central extension. Moreover, we show that under some conditions, two concepts of isoclinism and isomorphism between the relative central extensions of pairs of finite dimensional Lie algebras are coincide.

Mathematics Subject Classification (2010):

• Primary: 17B60
• Secondary: 17B40, 17B99

Key words:

• Pair of Lie algebras
• relative central extension
• isoclinism