The 2-nilpotent multiplier of n-Lie algebras and its applications

TL;DR

This paper investigates the structure and dimension of the 2-nilpotent multiplier in n-Lie algebras, providing formulas and applications for specific classes like abelian and Heisenberg n-Lie algebras.

Contribution

It introduces the structure of the 2-nilpotent multiplier for direct sums of n-Lie algebras and computes its dimension for various classes, extending previous theoretical frameworks.

Findings

Dimension formulas for abelian n-Lie algebras

Dimension of 2-nilpotent multiplier for Heisenberg n-Lie algebras

Structure of 2-nilpotent multiplier for direct sums of n-Lie algebras

Abstract

In this paper, we first recall the concept of c-nilpotent multiplier and c-capability of n-Lie algebras and also, recall the formula for calculating the number of basic commutators in n-Lie algebras. Then we give the structure of 2-nilpotent multiplier of the direct sum of two n-Lie algebras. Next, we calculate the dimension of 2-nilpotent multiplier of every abelian n-Lie algebras and Heisenberg n-Lie algebras H(n,m). Then we give a dimension of 2-nilpotent multiplier of any nilpotent n-Lie algebras of class 2 by using the number of basic commutators.