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Mathematics
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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On n-Derivations and n-Homomorphisms in Perfect Lie Superalgebras

Authors: Shakir Ali; Amal S. Alali; Mukhtar Ahmad; Md Shamim Akhter;

On n-Derivations and n-Homomorphisms in Perfect Lie Superalgebras

Abstract

Let n≥2 be a fixed integer. The aim of this paper is to investigate the properties of n-derivations within the framework of perfect Lie superalgebras over a commutative ring R. The main result shows that if the base ring contains 1n−1, and L is a perfect Lie superalgebra with a center equal to zero, then any n-derivation of L is necessarily a derivation. Additionally, every n-derivation of the derivation algebra Der(L) is an inner derivation. Moreover, we extend the concept of n-homomorphisms to mappings between Lie superalgebras L and L′ and prove that under specific assumptions, homomorphisms, anti-homomorphisms, and their combinations are all n-homomorphisms. Finally, we conclude our paper with some open problems.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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