What question did this study set out to answer?

The aim is to characterize all covers of n-Lie algebras and establish bounds for their Schur multipliers.

March 29, 2026Open Access

On the Schur Multiplier of n-Lie Algebras

Key Points

The aim is to characterize all covers of n-Lie algebras and establish bounds for their Schur multipliers.
Analyzed the structure of covers for n-Lie algebras with finite dimensional Schur multipliers.
Derived upper bounds for the dimension of the Schur multiplier M(A) of an n-Lie algebra A.
Developed a formula for the dimension of the Schur multiplier for the direct sum of two n-Lie algebras.
Established an upper bound for dim M(A) as d multiplied by n.
Demonstrated that this equality holds if and only if the n-Lie algebra A is abelian.
Provided a formula that links the Schur multiplier dimensions of direct sums of n-Lie algebras.

Abstract

In this article, we give the structure of all covers of n -Lie algebras with finite dimensional Schur multipliers, which generalizes an earlier work of Salemkar et.al.Also, For an n -Lie algebra A of dimension d , we find the upper bound dim M(A) d n , where M(A) denotes the Schur multiplier of A and that the equality holds if and only if A is abelian.Finally, we give a formula for the dimension of the Schur multiplier of the direct sum of two n -Lie algebras.

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