The nilpotent multipliers of the direct sum of Lie algebras

In this article, we present an explicit formula for the nilpotent multipliers of the direct sum of Lie algebras whose abelianisations are finite dimensional and, under some conditions, extend it for arbitrary Lie algebras. We also determine the nilpotent multipliers of some certain Lie algebras and obtain the exact structure of all c-capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.