On c-nilpotent multiplier and c-covers of a pair of Lie algebras

ABSTRACT

In this paper, we characterize the structure of the c-nilpotent multiplier of a pair of Lie algebras concerning the c-covering pairs and discuss some results on the existence of c-covers of a pair of Lie algebras. Moreover, we show that every nilpotent pair of Lie algebras of class at most k with non-trivial c-nilpotent multiplier does not admit any c-covering pair, if c>k. Also, we obtain the structure of c-covers of a c-capable pair of Lie algebras.

KEYWORDS:

• c-cover
• c-nilpotent multiplier
• pair of Lie algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 17B30, 17B60
• Secondary 17B99