$c$-nilpotent multiplier and $c$-capability of the direct sum of Lie algebras

TL;DR

This paper investigates how the $c$-nilpotent multiplier behaves under direct sums of Lie algebras and explores the $c$-capability of their finite-dimensional direct sums, providing new insights into their structural properties.

Contribution

It characterizes the behavior of the $c$-nilpotent multiplier and establishes results on the $c$-capability of direct sums of finite-dimensional Lie algebras.

Findings

The $c$-nilpotent multiplier's behavior under direct sums is explicitly determined.

Results on the $c$-capability of finite-dimensional Lie algebra direct sums are provided.

New structural properties of Lie algebras related to $c$-nilpotency are identified.

Abstract

In this paper, we determine the behavior of the $c$-nilpotent multiplier of Lie algebras with respect to the direct sums. Then we give some results on the $c$-capability of the direct sum of finite dimensional Lie algebras.